A catheter for insertion in a body orifice or blood vessel comprising an elongated tubular body with a soft, symmetrically deformable member on the distal end thereof for decreasing the likelihood of injury to body tissue upon the insertion and removal thereof. In one embodiment, the tip member comprises a toroidally shaped inflatable and non-distensible expandable "balloon" mounted on the end of the otherwise relatively rigid tip of the catheter. The catheter has a lumen extending the length thereof and communicating with the tip member whereby a fluid may be introduced to control the size, shape and firmness of the tip member. In a second embodiment, the soft deformable tip member comprises an annular plastic or rubber sleeve surrounding the otherwise rigid tip of the catheter and normally extending there beyond by a predetermined distance. The thickness or composition of the sleeve is varied about a circumferential ring so as to provide a preferred location for the collapse of the sleeve.