Aiming at the working characteristics of Nd∶YAG laser crystal with cooling system,mathematical physical model of heat conduction was designed.According to the mathematical physics method,the initial condition and the third boundary condition with air heat exchange coefficient,the heat transfer model of Nd∶YAG crystal material by using the knowledge of Bessel function and transcendental equation was solved,and the analytical solution expression of Nd∶YAG laser crystal temperature field was obtained.Based on the relationship between crystal thermal deformation and temperature field,the thermal deformation expression of working material was calculated .The temperature field and thermal deformation distribution of square Nd∶YAG crystals were defined and calculated.The influence of air heat exchange coefficient and other factors on the thermal deformation of crystal were analyzed.The simulation results are useful for the design and application of solid-state lasers.