The pump power stability range of solid-state laser resonators operating in the TEM//0//0 mode has been thoroughly investigated. It has been shown that for a very general resonator containing intracavity optical systems, rod thermal lensing engenders a pump power stability range that is a characteristic parameter of laser material and pump cavity but is independent of resonator configuration. Stability ranges have been calculated and critically discussed for Nd:YAG, Nd:glasses, Nd:Cr:GSGG, and alexandrite. The independence of the pump stability range from the resonator configuration has been experimentally demonstrated for a CW Nd:YAG laser.