The work aims to analyze force conditions on contact surface of yaw brake friction plate by referring to failure reason of the friction plate. Thermo-mechanical coupled contact model of brake disc and brake friction plate was established in finite element method. Parameters and material performance of the friction disc and brake disc were set. Stress and temperature distribution of the brake friction plate was studied provided with different pressure, sliding speed, friction coefficient and ambient temperature. Equivalent Mises stress and temperature distribution curves of the contact surface on the brake friction plate were obtained provided with yaw pressure, sliding speed, friction coefficient and ambient temperature. Both sides of the friction plate belonged to an alternating stress concentration zone of equivalent stress and temperature distribution, but were near edges, and equivalent stress and temperature values decreased slightly. Reducing pressure, increasing sliding speed and reducing friction coefficient helped reducing the equivalent Mises stress distribution of contact surface on friction plate. Temperature had no effect on the equivalent Mises stress distribution of contact surface on friction plate. Gauss distribution curve equation involving the equivalent Mises stress & temperature field and contact surface position of contact surface on friction plate was obtained. Correctness of finite element analysis was verified by comparing wear failure photos of the brake friction plate with calculating data in this paper. By choosing reasonable yaw pressure, sliding speed and friction coefficient, an alternating stress concentration zone of equivalent stress and temperature distribution can be effectively relieved for yaw brake friction plate, and service life of the friction plate can be prolonged.