The solid state heat capacity laser (SSHCL), as one of the most important high-power solid-state lasers, has attracted extensive attention. Numerical simulation of temperature and stress distributions of laser crystal slab in the heat capacity operation mode is a major means to understand the specific property of the laser. Using the method of plane stress approximation, the two-dimensional (2D) mathematical formulas that describe the temperature and stress distributions of laser diode (LD) pumped heat capacity slab laser are derived. Then the absorbed pump power density, 2D distributions of temperature and index of refraction are also analyzed and discussed. According to the results, the 2D distributions of temperature and stress are more homogeneous than that of the one-dimensional distributions.