A method of manufacturing a splittable/peelable tubular body of a catheter or sheath wherein the tubular body has a splittable/peelable atraumatic tip is disclosed. The atraumatic tip is generally softer than the tubular body. The tubular body and atraumatic tip each comprise a peel mechanism longitudinally extending along their respective lengths. The peel mechanisms are formed by longitudinally extending regions of interfacial bonding between first and second longitudinally extending strips of polymer material. Each strip forms at least a portion of an outer circumferential surface of the tubular body and atraumatic tip. A region of stress concentration extends along the region of interfacial bonding. The stress concentration facilitates the splitting of the tubular body and atraumatic tip along their respective peel mechanisms.