The magnetopause marks the outer edge of the Earth's magnetosphere and a distinct boundary between solar wind and magnetospheric plasma populations. In this study, we use global magnetohydrodynamic simulations to examine the response of the terrestrial magnetopause to fast‐forward interplanetary shocks of various strengths and compare to theoretical predictions. The theory and simulations indicate the magnetopause response can be characterized by three distinct phases; an initial acceleration as inertial forces are overcome, a rapid compressive phase comprising the majority of the distance traveled, and large‐scale damped oscillations with amplitudes of the order of an Earth radius. The two approaches agree in predicting subsolar magnetopause oscillations with frequencies 2–13 mHz but the simulations notably predict larger amplitudes and weaker damping rates. This phenomenon is of high relevance to space weather forecasting and provides a possible explanation for magnetopause oscillations observed following the large interplanetary shocks of August 1972 and March 1991.