The illustrative embodiment is a simulation system for practicing vascular-access procedures without using human subjects. The simulator comprises a data-processing system and a haptics device. The haptics device provides the physical interface at which an end effector, which is representative of a medical instrument (e.g., a needle, catheter, etc.), is manipulated with respect to a haptics-device base to simulate instrument insertion. The data-processing system, by exchanging signals with the haptics device, provides a three-dimensional simulation that includes the resistive forces that a medical practitioner would experience if the simulated procedure were an actual procedure that was being performed on a real anatomy (e.g., human arm, etc.). The simulator displays the ongoing simulation and assesses the performance of its user.