Mathematical modeling, based on rate equations, is used to estimate the theoretical limits of the emission efficiency of 3-μm Er:YAG laser in various generation regimes. This model uses exclusively spectroscopic data and includes upconversion from both initial (4I11/2) and terminal 4Il3/2) laser levels and cross-relaxation from the 4S3/2 level. The energy transfer processes, very active at high erbium concentrations, assure the re-circulation of the excitation on the metastable levels of Er3+, leading to supraunitary quantum efficiency and high emission efficiency in CW regime. In contrast with the CW (and free-generation) regime, the energy transfer processes are frozen during the generation of the giant pulse in Q-switch regime, limiting severely the access to the stored energy. As a consequence, the efficiency in Q-switch is low. We find simple analytic expressions for the emission efficiency in CW, free-generation and Q-switch regimes. We compare the results of the modeling with the available experimental results. Finally, some suggestions to improve the overall efficiency of the 3-μm erbium lasers working in Q-switch regime are given.