We have performed a number of numerical experiments to study the interaction of interstellar pickup protons and helium ions with quasi‐parallel stationary (bow) shocks and interplanetary traveling shocks. The collisionless shocks are modeled by the hybrid simulation method which treats the ions as macroparticles and the electrons as a massless background fluid. Solar wind protons, alpha particles, pickup H+ and He+ are included self‐consistently. The pickup ion distributions are modeled as spherical shells in velocity space convected with the solar wind. Pickup ions are rather efficiently reflected at both types of shocks. The reflection coefficient, measured as the ratio of incident to reflected ions, is more than one order of magnitude larger than the reflection coefficients for either solar wind protons or alpha particles, and is of the order of 30%. We have found that at high Mach number shocks pickup ions can reach many tens to over hundred times the plasma ramming energy in essentially one shock encounter. The reflected pickup ion distributions have a pancake‐type shape in velocity space.