Surface pressure measurements on Mars have revealed a wide variety of atmospheric phenomena. The Mars Science Laboratory Rover Environmental Monitoring Station pressure sensor data set is now the longest duration record of surface pressure on Mars. We use the first 2580 Martian sols, nearly 4 Mars years, of measurements to identify atmospheric pressure waves with periods of tens of minutes to hours using wavelet analysis on residual pressure after the tidal harmonics are removed. We find these waves have a clear diurnal cycle with strongest activity in the early morning and late evening and a seasonal cycle with the strongest waves in the second half of the martian year (Ls = 180–360°). The strongest such waves of the entire mission occurred during the Mars Year 34 global dust storm. Comparable atmospheric waves are identified using atmospheric modeling with the MarsWRF general circulation model in a “nested” high spatial resolution mode. With the support of the modeling, we find these waves best fit the expected properties of inertia-gravity waves with horizontal wavelengths of O(100s) of km.