Laser diode (LD) end-pumped square YAG/Yb∶YAG composite crystal is taken as the study specimen. Based on the theory of heat conduction and working characteristics of continuous LD end-pumped square YAG/Yb∶YAG, the effects of pump power, thickness, and section size of YAG crystal on temperature, thermal stress, and thermal deformation of laser crystal is systematically investigated using finite element method. The pump spot radius of collimation focused using an optical coupling system is 400 μm in the calculation process. The findings show that when the size of Yb∶YAG crystal is 4 mm×4 mm×1 mm, and the thickness of YAG crystal is 0.1 mm, the maximum temperature rise in YAG/Yb∶YAG square crystal increases from 37.19 ℃ to 82.92 ℃ with the increase in pump power from 60 W to 80 W. When the YAG crystal's thickness increases from 0 mm to 0.5 mm, the maximum thermal stress changes from 26.93 MPa to 10.438 MPa, and the maximum temperature decreases by 18.18 ℃, but the thermal deformation due to thermal stress remains unchanged. The use of square YAG/Yb∶YAG composite crystal can efficiently decrease the maximum thermal stress and temperature rise in laser crystal, which has guiding significance for the design and high power output of all-solid Yb∶YAG laser.