The interaction of upstream pressure pulses with the Earth's bow shock and their propagation through the magnetosheath are studied by means of one-dimensional hybrid (particle ions, massless fluid electrons) simulations. The pulses either are generated self-consistently as a result of the presence of ions streaming away from the quasi-parallel shock or are created artificially through density or velocity perturbations in the solar wind some distance upstream of the shock so that interaction of pressure pulses with both the quasi-parallel and quasi-perpendicular portion of the bow shock can be investigated. We demonstrate that the pulses tend to perturb the shock structure only for a limited time and then propagate in a coherent manner at the magnetosonic speed for large distances (>5RE) downstream of the shock. Implications for the intersection of such pulses with the magnetopause are also addressed. ¿ American Geophysical Union 1995