Abstract: Vascular access catheters that include a catheter body having one or a plurality of lumens longitudinally extending therethrough. The lumens have cross-sectional shapes that enhance kink resistance, support reliable slit valve operation, and couple securely with the outlet stem of a multiple reservoir implantable access port. In a dual lumen catheter disclosed, each of the lumens are defined by a plurality of longitudinally extending generally linear inner wall surfaces. The inner wall surfaces when viewed in a transverse cross section of the catheter body taken normal to the longitudinal access have trapezoidal shapes. Other cross-sectional shapes are also illustrated. A generally planar septum separates the pair of lumens. The lumens effect a fluid-tight mechanical engagement between the D-shaped outlet prongs of a conventional outlet stem of an implantable dual reservoir access port, highly reliable two-way, three-position slit valves may be associated with each of the lumens.