A mathematical model, based exclusively on spectroscopic data concerning radiative, non-radiative, and energy transfer processes, is proposed and used to simulate the Q-switch regime of three-micron Er:YAG laser. The connection between the main energy transfer mechanisms that make possible generation on the self-saturated transition 4I11/2 yields 4I13/2 (up- conversion from 4I13/2 and 4I11/2, cross- relaxation from 4S3/2) and the giant pulse characteristics is discussed. The radiative as well as non- radiative losses during optical pumping and giant pulse generation are defined and evaluated. A particular attention is given to FTIR Q-switch which demonstrated real qualities for 3- micrometers Erbium lasers. The reasons responsible for experimental performances of Q-switched Er:YAG lasers inferior to those predicted by the mathematical modeling are analyzed.