Exhibit 4.1

  THE TERMS AND CONDITIONS OF THE RIGHTS OFFERING
    ARE SET FORTH IN THE COMPANY’S PROSPECTUS DATED AUGUST 21, 2020, AS SUPPLEMENTED BY THE PROSPECTUS SUPPLEMENT DATED MAY 4, 2022
    (COLLECTIVELY, THE “PROSPECTUS”) AND ARE INCORPORATED HEREIN BY REFERENCE. COPIES OF THE PROSPECTUS ARE AVAILABLE UPON REQUEST
    FROM BROADRIDGE CORPORATE ISSUER SOLUTIONS, INC., THE SUBSCRIPTION AGENT, BY CALLING (888) 789-8409.

  PULSE BIOSCIENCES, INC.

    Incorporated under the laws of the State of Delaware

  NON-TRANSFERABLE SUBSCRIPTION RIGHTS CERTIFICATE

  Evidencing Non-Transferable Subscription Rights to Purchase Units
    of Pulse Biosciences, Inc.

    Subscription Price: To be determined as set forth below

  THE SUBSCRIPTION RIGHTS WILL EXPIRE IF NOT EXERCISED
    ON OR BEFORE

    5:00 P.M., EASTERN TIME, ON MAY 23, 2022 (THE “EXPIRATION DATE”)

  REGISTERED OWNER:

  THIS CERTIFIES THAT the registered owner whose
    name is inscribed hereon is the owner of the number of non-transferable subscription rights (“Rights”) set forth above.
    The Rights entitle the holder thereof to subscribe for and purchase units of Pulse Biosciences, Inc., a Delaware corporation (the “Company”),
    each unit consisting of one share of common stock, par value $0.001 per share (the “Common Stock”) and a warrant to
    purchase one share of Common Stock, only during a limited time (the “Units”, and each, a “Unit”),
    at a subscription price per full Unit equal to the lesser of (i) $3.72 (the “Initial Price”) and (ii) the volume
    weighted average price of the Common Stock for the five trading day period through and including the Expiration Date (the “Alternate
      Price”), pursuant to a rights offering (the “Rights Offering”), on the terms and subject to the conditions
    set forth in the prospectus dated August 21, 2020, as supplemented by the prospectus supplement dated May 4, 2022 (collectively, the “Prospectus”).

  Each Right includes a subscription right. Under
    the subscription right, for each share of common stock owned as of the record date of the Rights Offering, the holder hereof is entitled
    to purchase 0.13530032 Units at the Initial Price per full Unit.

  The Rights represented by this Subscription Rights
    Certificate may be exercised by completing Section 1 and any other appropriate sections herein and by returning the full payment of the
    subscription price for each Unit in accordance with the instructions contained herein. If, on the Expiration Date, the Alternate Price
    is lower than the Initial Price, any excess subscription amounts paid will be put towards the purchase of additional Units (either towards
    basic subscription rights, if available, or towards the over-subscription right if the basic subscription rights have already been exercised
    in full).

  This Non-Transferable Subscription Rights Certificate
    is not valid unless countersigned by Broadridge Corporate Issuer Solutions, Inc., the Subscription Agent. Witness the seal of Pulse Biosciences,
    Inc. and the signatures of its duly authorized officers.

  DATED: May 4, 2022

  	 	​	​	 
	President and Chief Executive Officer	​	​	
          Secretary

        


  

  

  
  

  

  
    
      


  

  DELIVERY OPTIONS FOR NON-TRANSFERABLE SUBSCRIPTION RIGHTS CERTIFICATE

  Deliver other than in the manner or to the addresses listed below will not constitute valid delivery.

  	If delivering by hand or overnight courier:	​	​	If delivering by first class mail:
	 	​	​	 
	Broadridge Corporate Issuer Solutions, Inc.

            Attn: BCIS IWS

            51 Mercedes Way

            Edgewood, NY 11717	​	​	Broadridge Corporate Issuer Solutions, Inc.

            Attn: BCIS Re-Organization Dept.

            P.O. Box 1317

            Brentwood, NY 11717-0718


  PLEASE PRINT ALL INFORMATION CLEARLY AND LEGIBLY.

  SECTION 1 – EXERCISE OF SUBSCRIPTION RIGHTS

  To subscribe for Units pursuant to your Rights,
    please complete lines (a) and (b) and sign in part (c). If you do not indicate the number of Rights being exercised, or if you do not
    forward the full subscription payment for the number of Rights that you indicate are being exercised, then you will be deemed to have
    exercised the maximum number of Rights that may be exercised with the aggregate subscription payment you timely delivered to the Subscription
    Agent. Fractional Units resulting from the exercise of the subscription rights will be eliminated by rounding down to the nearest whole
    number, with the total subscription payment being adjusted accordingly. Any excess subscription payments received by the Subscription
    Agent will be returned, without interest, as soon as practicable. The common stock and warrants comprising the Units will separate upon
    the closing of the rights offering and will be issued separately, however, they may only be purchased as a Unit and the Units will not
    trade as a separate security. Each warrant will be exercisable for one share of Common Stock at an exercise price equivalent to the subscription
    price through its expiration five years from the date of issuance. The number of warrants issued to you will be calculated by rounding
    down to the nearest whole number the number of Units you subscribe for.

  	(a)	EXERCISE OF SUBSCRIPTION RIGHT:


  

  

  	 	(i)	Basic Subscription Rights:


  

  

  	 I exercise	​	 	​	x	​	0.13530032	​	=	​	 	​	x	​	$3.72	​	=	​	$
	 	​	(No. of shares owned)	​	x	​	
          (Initial ratio)

           

           

        	​	=	​	(No. of Basic Subscription Units Subscribed For)	​	x	​	(Initial Price)	​	 	​	(Amount Enclosed)


  

  

  	 	(ii)	Over-Subscription Right: If you fully exercise your Basic Subscription Right, above, and wish to subscribe for additional shares, you
            may exercise your Over-Subscription Right below.


  

  

  	 I exercise	​	 	​	x	​	$3.72	​	=	​	$	 
	 	​	 	​	 	​	 	​	 	​	 	 
	 	​	(No. of Over-Subscription Units Subscribed For)	​	x	​	(Initial Price)	​	=	​	(Amount Enclosed)	 


  

  

  
  
     

    
      
        


    

  

  
  

  

  	(b)	PAYMENT:


  

  

  	 	​	​	Amount Enclosed	​	​	 
	 	 	 	 	 	 	 
	Basic Subscription Right:	​	​	$	​	​	 
	​	 	​
	 	​	​	 	​
	Over-Subscription Right:	​	​	$	​	​	 
	​	 	​
	 	​	​	 	​
	Total Amount Enclosed:	​	​	$	​	​	 
	​	 	​	​	 


  Method of Payment: All payments must be made in U.S. dollars
    by wire transfer of funds, U.S. Postal money order or cashier’s, certified, or uncertified check drawn upon a U.S. bank payable
    to “Broadridge Corporate Issuer Solutions, Inc. (acting as Subscription Agent for Pulse Biosciences Inc.).” The Subscription
    Agent will not accept payment by any other means. Please indicate how you are making payment:

  	 ☐ Check or bank draft drawn on a U.S. bank, or postal or express money order payable to Broadridge Corporate Issuer Solutions, Inc., as Subscription Agent.	 
	 
	 
	 ☐ Wire transfer directly to the escrow account maintained by Broadridge Corporate Issuer Solutions, Inc., as Subscription Agent.	 


  

  

  	(c)	SIGNATURE(S):	 	 


  TO SUBSCRIBE: I acknowledge that I have received
    the Prospectus for the rights offering and I hereby irrevocably subscribe for the number of Units indicated above on the terms and conditions
    specified in the Prospectus. I hereby agree that if I fail to pay for the Units for which I have subscribed, Pulse Biosciences, Inc. may
    exercise its legal remedies against me.

  This form must be signed by the registered holder(s)
    exactly as their name(s) appear(s) on the certificate(s) or book entry or by person(s) authorized to sign on behalf of the registered
    holder(s) by documents transmitted herewith.

  	 	​	 	​	 
	Signature(s) of Subscriber(s)	​	Date	​	Daytime Telephone Number(s)


  If signature is by trustee(s), executor(s), administrator(s),
    guardian(s), attorney(s)-in-fact, agent(s), officer(s) of a corporation, or another acting in a fiduciary or representative capacity,
    please provide the following information (please print). See the instructions.

  	 	​	 	​	 	​	 
	Name(s)	​	Full Title	​	Taxpayer ID # or Social Security #	​	Date


  

  

  
     

  
    
      


  

  
  SECTION 2 – SPECIAL ISSUANCE OR DELIVERY INSTRUCTIONS FOR SUBSCRIPTION RIGHTS HOLDERS

  	
          (a)    To be completed ONLY if the book-entry
              representing the Common Stock is to be issued in a name other than that of the registered holder. (See the Instructions.)

          DO NOT FORGET TO COMPLETE THE GUARANTEE OF SIGNATURE(S) SECTION BELOW.

        	​	​	 	​	​	
          (b)    To be completed ONLY if the book-entry
              representing the Common Stock is to be issued to an address other than that shown on the front of this certificate. (See the Instructions.)

          DO NOT FORGET TO COMPLETE THE GUARANTEE OF SIGNATURE(S) SECTION BELOW.

        


  

  

  	Print Full Name:	​	 	​	Print Full Name:	​	 
	Print Full Address:	​	 	​	Print Full Address:	​	 
	Taxpayer ID # or

            Social Security #:	​	 	​	Taxpayer ID # or

            Social Security #:	​	 


  SIGNATURE GUARANTEE

    This must be completed if you have completed any portion of Section 2.

  	Signature Guaranteed:	​	 	​	 
	 	​	(Name of Bank or Form)	​	 


  	By:	​	 	​	 
	 	​	  (Signature of Officer)	​	 


  

    IMPORTANT: The signature(s) should be guaranteed by an eligible guarantor institution (bank, stock broker, savings & loan association
    or credit union) with membership in an approved signature guarantee medallion program pursuant to Securities and Exchange Commission Rule
    17Ad-15.

  FOR INSTRUCTIONS ON THE USE OF NON-TRANSFERABLE
    SUBSCRIPTION RIGHTS CERTIFICATES, CONSULT BROADRIDGE CORPORATE ISSUER SOLUTIONS, INC., THE SUBSCRIPTION AGENT, AT (888) 789-8409 (TOLL-FREE).
    THE RIGHTS OFFERING EXPIRES AT 5:00 P.M., EASTERN TIME, ON MAY 23, 2022, AND THIS NON-TRANSFERABLE SUBSCRIPTION RIGHTS CERTIFICATE
    IS VOID THEREAFTER.

  THE RIGHTS OFFERING HAS BEEN REGISTERED OR QUALIFIED
    OR IS BELIEVED TO BE EXEMPT FROM REGISTRATION OR QUALIFICATION ONLY UNDER THE FEDERAL LAWS OF THE UNITED STATES AND THE LAWS OF STATES
    IN THE UNITED STATES. RESIDENTS OF OTHER JURISDICTIONS MAY NOT PURCHASE THE SECURITIES OFFERED HEREBY UNLESS THEY CERTIFY THAT THEIR PURCHASES
    OF SUCH SECURITIES ARE EFFECTED IN ACCORDANCE WITH THE APPLICABLE LAWS OF SUCH JURISDICTIONS.