Based on the theory of thermal analysis, heat conduction equation of Nd∶LuVO4 crystal slab side-pumped by diode laser arrays is built. By solving the heat conduction equation, the analytic expression of temperature field and thermal deformation distribution is obtained. When geometry of pumping diodes corresponds to 1 mm×4 mm, and the power is about 40 W, temperature and heat deformation field of numerical simulation results show that the maximum temperature rise of 11.63 K along x, and 11.00 K along y and z direction, respectively, and total thermal deformations are 0.050 μm, 0.034 μm and 0.48 μm along x, y and z direction, respectively. This work will supply the theory for design of Nd∶LuVO4 laser.