Thermal effect of Nd:YAG slab gain medium is studied for solid slab high power amplifier. The investigation uses the finite element method to simulate the distribution of temperature and stress of Nd:YAG slab gain medium with edge pump by high power laser diode array, considering uneven pump distribution in gain medium. The result shows that the temperature and stress of the bonding part of doped and undoped YAG are the highest. It is the weakness of the slab gain medium and should be designed optimum for avoiding slab Nd:YAG damage . Refer to the result, the power amplifier is designed. The laser chain is built, and the seed laser of 2.5 W power is amplified by a four-pass pre-amplifier and four stage double-pass power amplifier. The laser chain achieves 11 kW laser average power. The temperature distribution of slab gain medium with high power pump is measured in the experiment. The experimental result agrees well with the simulation.