Ownership Submission
FORM 4
Check this box if no longer subject to Section 16. Form 4 or Form 5 obligations may continue. See Instruction 1(b).
UNITED STATES SECURITIES AND EXCHANGE COMMISSION
Washington, D.C. 20549

STATEMENT OF CHANGES IN BENEFICIAL OWNERSHIP OF SECURITIES

Filed pursuant to Section 16(a) of the Securities Exchange Act of 1934, Section 17(a) of the Public Utility Holding Company Act of 1935 or Section 30(h) of the Investment Company Act of 1940
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(Print or Type Responses)
1. Name and Address of Reporting Person *
PERRY EDWARD N
   2. Issuer Name and Ticker or Trading Symbol
BEMIS CO INC [BMS] 		5. Relationship of Reporting Person(s) to Issuer
(Check all applicable)
__X__ Director _____ 10% Owner
_____ Officer (give title below) _____ Other (specify below)
(Last)
(First)
(Middle)
ONE NEENAH CENTER, 4TH FLOOR, P.O. BOX 669		 3. Date of Earliest Transaction (Month/Day/Year)
05/01/2008
(Street)

NEENAH, WI 54957		 4. If Amendment, Date Original Filed(Month/Day/Year)
 6. Individual or Joint/Group Filing(Check Applicable Line)
_X_ Form filed by One Reporting Person
___ Form filed by More than One Reporting Person
(City)
(State)
(Zip)
Table I - Non-Derivative Securities Acquired, Disposed of, or Beneficially Owned
1.Title of Security
(Instr. 3)		 2. Transaction Date (Month/Day/Year) 2A. Deemed Execution Date, if any (Month/Day/Year) 3. Transaction Code
(Instr. 8)		 4. Securities Acquired (A) or Disposed of (D)
(Instr. 3, 4 and 5)		 5. Amount of Securities Beneficially Owned Following Reported Transaction(s)
(Instr. 3 and 4)		 6. Ownership Form: Direct (D) or Indirect (I)
(Instr. 4)		 7. Nature of Indirect Beneficial Ownership
(Instr. 4)
Code V Amount (A) or (D) Price
Common Stock 05/01/2008   A   1,224 (7) A $ 26.57 259,958 D  
Common Stock 05/05/2008   M   1,815 (4) A $ 26.36 261,773 D  
Common Stock               4,000 (1) D  
Common Stock               7,600 (2) D  

Reminder: Report on a separate line for each class of securities beneficially owned directly or indirectly.
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Table II - Derivative Securities Acquired, Disposed of, or Beneficially Owned
(e.g., puts, calls, warrants, options, convertible securities)
1. Title of Derivative Security
(Instr. 3)		 2. Conversion or Exercise Price of Derivative Security 3. Transaction Date (Month/Day/Year) 3A. Deemed Execution Date, if any (Month/Day/Year) 4. Transaction Code
(Instr. 8)		 5. Number of Derivative Securities Acquired (A) or Disposed of (D)
(Instr. 3, 4, and 5)		 6. Date Exercisable and Expiration Date
(Month/Day/Year)		 7. Title and Amount of Underlying Securities
(Instr. 3 and 4)		 8. Price of Derivative Security
(Instr. 5)		 9. Number of Derivative Securities Beneficially Owned Following Reported Transaction(s)
(Instr. 4)		 10. Ownership Form of Derivative Security: Direct (D) or Indirect (I)
(Instr. 4)		 11. Nature of Indirect Beneficial Ownership
(Instr. 4)
Code V (A) (D) Date Exercisable Expiration Date Title Amount or Number of Shares
Common Stock (3) 05/05/2005 05/05/2008 M     1,815 05/05/2008(4) 05/05/2008 Common Stock 1,815 (8) 0 D  
Common Stock (3) 05/04/2006   A   797   05/04/2009(5) 05/04/2009 Common Stock 797 (8) 797 D  
Common Stock (3) 05/03/2007   A   963   05/03/2010(6) 05/03/2010 Common Stock 963 (8) 963 D  
Phantom Stock (9) 10/01/1996   A   42.705     (10)   (10) Phantom Stock 42.705 $ 35.125 42.705 D  
Phantom Stock (9) 12/31/1997   A   146.907     (10)   (10) Phantom Stock 146.907 (11) 146.907 D  
Phantom Stock (9) 12/31/1998   A   224.28     (10)   (10) Phantom Stock 224.28 (12) 224.28 D  
Phantom Stock (9) 12/31/1999   A   286.503     (10)   (10) Phantom Stock 286.503 (13) 286.503 D  
Phantom Stock (9) 12/31/2000   A   291.656     (10)   (10) Phantom Stock 291.656 (14) 291.656 D  
Phantom Stock (9) 12/31/2001   A   277.924     (10)   (10) Phantom Stock 277.924 (15) 277.924 D  
Phantom Stock (9) 12/31/2002   A   42.585     (10)   (10) Phantom Stock 42.585 (16) 42.585 D  
Phantom Stock (9) 12/31/2003   A   53.944     (10)   (10) Phantom Stock 53.944 (17) 53.944 D  
Phantom Stock (9) 12/31/2004   A   105.594     (10)   (10) Phantom Stock 105.594 (18) 105.594 D  
Phantom Stock (9) 12/31/2005   A   117.249     (10)   (10) Phantom Stock 117.249 (19) 117.249 D  
Phantom Stock (9) 12/31/2006   A   111.11     (10)   (10) Phantom Stock 111.11 (20) 111.11 D  
Phantom Stock (9) 12/31/2007   A   130.839     (10)   (10) Phantom Stock 130.839 (21) 130.839 D  
Phantom Stock (9) 03/03/2008   A   43.139     (10)   (10) Phantom Stock 43.139 (22) 4,901.995 (23) D  

Reporting Owners

Reporting Owner Name / Address Relationships
 Director  10% Owner  Officer  Other
PERRY EDWARD N
ONE NEENAH CENTER, 4TH FLOOR
P.O. BOX 669
NEENAH, WI 54957		   X      

Signatures

 J J Seifert Power of Attorney   05/05/2008
**Signature of Reporting Person Date

Explanation of Responses:

* If the form is filed by more than one reporting person, see Instruction 4(b)(v).
** Intentional misstatements or omissions of facts constitute Federal Criminal Violations. See 18 U.S.C. 1001 and 15 U.S.C. 78ff(a).
(1) Direct Ownership with Spouse.
(2) Direct Ownership with Children.
(3) Security converts to Common Stock on a one-for-one basis on date of conversion.
(4) Stock Award granted to Bemis Director pursuant to 2001 Stock Incentive Plan exempt under Rule 16b-3: Grant to Reporting Person of right to receive stock as of May 5, 2008. Payout of 1,815 shares was made on May 5, 2008.
(5) Stock Award granted to Bemis Director pursuant to 2001 Stock Incentive Plan exempt under Rule 16b-3: Grant to Reporting Person of right to receive stock as of May 4, 2009.
(6) Stock Award granted to Bemis Director pursuant to 2007 Stock Incentive Plan exempt under Rule 16b-3: Grant to Reporting Person of right to receive stock as of May 3, 2010.
(7) Stock Award granted to Bemis Director pursuant to 2007 Stock Incentive Plan exempt under Rule 16b-3: Grant made to Director on May 1, 2008 as part of Directors' Annual Fee.
(8) Will know price on the date of conversion.
(9) Phantom Stock units convert to one share of Common Stock. On date of payout, distribution is made in cash equivalent to value of Phantom Stock units.
(10) In a single lump sum distribution in January following termination of service as a Director.
(11) Acquired at various dates from January 1, 1997 to December 31, 1997 at prices ranging from $35.875 to $44.875.
(12) Acquired at various dates from January 1, 1998 to December 31, 1998 at prices ranging from $33.9375 to $45.125.
(13) Acquired at various dates from January 1, 1999 to December 31, 1999 at prices ranging from $31.9375 to $38.3125.
(14) Acquired at various dates from January 1, 2000 to December 31, 2000 at prices ranging from $31.75 to $36.5625
(15) Acquired at various dates from January 1, 2001 to December 31, 2001 at prices ranging from $32.1875 to $49.99.
(16) Acquired at various dates from January 1, 2002 to December 31, 2002 at prices ranging from $48.26 to $56.78.
(17) Acquired at various dates from January 1, 2003 to December 31, 2003 at prices ranging from $41.26 to $46.48.
(18) Acquired at various dates from January 1, 2004 to December 31, 2004 at prices ranging from $25.81 to $27.85.
(19) Acquired at various dates from January 1, 2005 to December 31, 2005 at prices ranging from $26.02 to $30.36.
(20) Acquired at various dates from January 1, 2006 to December 31, 2006 at prices ranging from $30.01 to $34.08.
(21) Acquired at various dates from January 1, 2007 to December 31, 2007 at prices ranging from $26.87 to $33.78.
(22) Acquired on March 3, 2008 at a price of $24.78.
(23) For ALL Phantom Stock (combined - listed above, including the March 2004 Two-for-One Stock Split)- quarterly dividends increase the amount in Column 5(a) to this total number of derivative securities as of the date of this filing.

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