Thermal management in solid state laser is a challenge to the high power laser industry’s ability to provide continued improvements in device and system performance. In this work an investigation of heat generation and thermo-mechanical effect in a high-power Nd:YAG and Yb:YAG cylindrical-type solid state laser pumped longitudinally with different power by fibre coupled laser diode is carried out by numerical simulation based on the finite element method (FEM). Impact of the dopant concentration on the power conversion efficiency is included in the simulation. The distribution of the temperature inside the lasing material is resolute according to the thermal conductivity. The thermo-mechanical effect is explored as a function of pump power in order to determine the maximum pumping power allowed to prevent the crystal’s fracture. The presented simulations are in broad agreement with analytical solutions; provided that the boundary condition of the pump induced heat generation is accurately modelled.