The optimal physical conditions of single-longitudinal-mode (SLM) operation for continuous-wave all-solid-state lasers with high output powers are investigated theoretically and experimentally. The dependence of the operation conditions on the linear and nonlinear intracavity losses of the laser is numerically calculated. The theoretical analysis is demonstrated by the experimental measurements on a home-made Nd:YVO4 laser. The stable SLM output up to 33.7 W with optical-optical conversion efficiency of 44.9% at 1064 nm wavelength is recorded for over 7 h. The experimental results are in good agreement with the theoretical expectation.