An irrigation/aspiration needle has a rigid needle body over which an elastomeric sleeve is fitted. The elastomeric sleeve terminates in a smooth, relatively soft, rounded tip through which a passageway extends, communicating with a passageway in the sleeve which, in turn, communicates with passageways in the needle body and needle mount, forming a liquid flow path through the needle. The softness of the elastomeric sleeve and, particularly, the sleeve tip protects delicate eye tissue when the needle is used for aspiration from or irrigation of the eye during surgery.