Growth of lithium dendrites in solid state batteries is an important factor that disturbs their commercial applications. The growth of lithium dendrites at the interface of lithium metal anode will not only lead to the decrease of battery energy efficiency, but also cause combustion, explosion and other safety problems. In order to explore the factors and methods that inhibit the growth of lithium dendrites, the phase-field theory is used to simulate the growth of lithium dendrites in polymer solid electrolyte batteries, and a phase-field model of lithium dendrite growth coupled with mechanical stress and thermal field is established. The effects of key physical factors such as ambient temperature, solid electrolyte Young’s modulus and external stress on dendrite growth and their acting principles are discussed and analyzed. The results show that under the conditions of high temperature, high solid electrolyte Young’s modulus and external stress, the growth of lithium dendrites is slow, the number of long dendrites is small, and the electrodeposition is more uniform. In addition, the effects of Young’s modulus of solid electrolyte and ambient temperature on the growth of lithium dendrites in a common range are compared with each other. It is found that the inhibition effect of changing Young’s modulus of solid electrolyte on the maximum length of lithium dendrites is 19% higher than that caused by the change of ambient temperature.