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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1. Name and Address of Reporting Person * SCHOLLE WILLIAM J   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) SUITE 2300, 222 S. 9TH ST. 3. Date of Earliest Transaction (Month/Day/Year) 05/02/2006 (Street) MINNEAPOLIS, MN 55402-4099 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 05/02/2006   M   1,968 (4) A $ 31.39 4,268 D

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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

$ 22.035

08/02/2001

A

7,700

(1)

08/02/2011

Common Stock

7,700

(2)

7,700

D

Common Stock

(3)

05/02/2003

05/02/2006

M

1,968

05/02/2006(4)

05/02/2006

Common Stock

1,968

(7)

0

D

Common Stock

(3)

05/05/2005

A

1,815

05/05/2008(5)

05/05/2008

Common Stock

1,815

(7)

1,815

D

Common Stock

(3)

05/04/2006

A

797

05/04/2009(6)

05/04/2009

Common Stock

797

(7)

797

D

Reporting Owners

Reporting Owner Name / Address	Relationships
	Director	10% Owner	Officer	Other
SCHOLLE WILLIAM J SUITE 2300 222 S. 9TH ST. MINNEAPOLIS, MN 55402-4099	X

Signatures

J J Seifert Power of Attorney		05/04/2006
**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)	Stock Option (Right to Buy) granted pursuant to Bemis Director's Stock Option Program exempt under Rule 16b-3: All options now exercisable.
(2)	Will know price on the date of exercise.
(3)	Security converts to Common Stock on a one-for-one basis on date of converson.
(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 2, 2006. Payout of 1,968 shares was made on May 2, 2006.
(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 5, 2008.
(6)	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.
(7)	Will know price on date of conversion.

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