A splittable/peelable tubular body (2) of a catheter or sheath wherein the tubular body (2) has a splittable/peelable atraumatic tip (14) is disclosed. The atraumatic tip (4) is generally softer than the tubular body (2). The tubular body (2) and atraumatic tip (4) each comprise a peel mechanism longitudinally extending along their respective lengths. The peel mechanisms are formed by longitudinally extending regions of interfacial bonding (11) between first and second longitudinally extending strips (8, 10) of polymer material. Each strip (8, 10) forms at least a portion of an outer circumferential surface of the tubular body (2) and atraumatic tip (4). A region of stress concentration extends along the region of interfacial bonding. The stress concentration facilitates the splitting of the tubular body (2) and atraumatic tip (4) along their respective peel mechanisms.