A catheter assembly including an internal bolster. According to one embodiment, the catheter assembly includes a medical catheter preferably made of extruded silicone rubber. The catheter is shaped to include a cylindrical wall defining a primary longitudinal bore. A plurality of secondary longitudinal bores is provided in the cylindrical wall, the secondary bores being evenly spaced around the primary bore. The assembly also includes a plurality of identical resilient members collectively forming an anchor at a first end of the catheter. Each resilient member comprises a resilient wire and a protective jacket. Each wire is made of a shape-memory material and is reversibly transformable between a spiral shape, when at rest, and a straightened shape, when forcibly unfurled. One end of each wire is disposed within a secondary bore of the catheter, with the remainder of each wire extending out from the catheter. Each jacket is preferably made of silicone rubber and encapsulates all of the length of its wire, except for the small portion of the wire inserted into the bore.