In order to analyze the amplification propertied of cryogenic Yb:YAG amplifier, based on pumping dynamics and pulse amplification performance, the ampification properties of cryogenics Yb:YAG amplifier is researched in simulation. The amplification performance on different size and concentration of crystal and different temperature and pumping power density is calculated. 3D thermal analysis model is used to simulate the thermal management effect. The results demonstrate that the pump power density, the size of laser medium and the temperature all have distinct effect on the optical to optical efficiency. In the temperature range of 100 K to 300 K, the optimal working temperature increase with the pump power density. With the same pump power density, the medium with different size have different optimal working temperature. In the condition of low temperature and strong pump, the thicker crystal has a better thermal management effect than a thinner crystal.