The explicit analytical expressions of pump absorption efficiency,slope efficiency,fundamental-wave geometric average intensity in cavity,laser threshold,output laser intensity and power for longitudinally-pumped quasi-three-level continuous-wave lasers have been derived using the rate equations and optical transmission equations in cavity.Furthermore,the influences of laser-induced pump absorption saturation effect on pump absorption efficiency,laser threshold,conversion efficiency and fundamental-wave geometric average intensity in cavity are discussed.Theoretical analysis and numerical simulations indicate that the influences of the pump absorption saturation on the performance of lasers relate to the ratio of the pump absorption cross section and laser stimulated emission cross section,the average single-pass loss factor,the population factors of pump energy level and upper and lower laser energy levels,length of laser crystal,etc.When the laser crystal is shorter,the average single-pass loss factor is larger,the ratio of pump absorption cross section and laser stimulated emission cross section is larger,and the pump absorption saturation effect is more obvious.The decline of the pump absorption efficiency results in the increase of the laser threshold and the decrease of the fundamental-wave geometric average intensity in cavity and laser conversion efficiency.