Forbush decreases are depressions in the galactic cosmic rays (GCRs) that are caused primarily by modulations of interplanetary coronal mass ejections (ICMEs) but also occasionally by stream/corotating interaction regions (SIRs/CIRs). Forbush decreases have been studied extensively using neutron monitors at Earth; recently, for the first time, they have been measured on the surface of another planet, Mars, by the Radiation Assessment Detector (RAD) on board the Mars Science Laboratory’s (MSL) rover Curiosity. The modulation of GCR particles by heliospheric transients in space is energy-dependent; afterwards, these particles interact with the Martian atmosphere, the interaction process depending on particle type and energy. In order to use ground-measured Forbush decreases to study the space weather environment near Mars, it is important to understand and quantify the energy-dependent modulation of the GCR particles by not only the pass-by heliospheric disturbances but also by the Martian atmosphere. Accordingly, this study presents a model that quantifies — both at the Martian surface and in the interplanetary space near Mars — the amplitudes of Forbush decreases at Mars during the pass-by of an ICME/SIR by combining the heliospheric modulation of GCRs with the atmospheric modification of such modulated GCR spectra. The modeled results are in good agreement with measurements of Forbush decreases caused by ICMEs/SIRs based on data collected by MSL on the surface of Mars and by the Mars Atmosphere and Volatile EvolutioN (MAVEN) spacecraft in orbit. Our model and these findings support the validity of both the Forbush decrease description and Martian atmospheric transport models.