We demonstrated a high power and good beam quality continuous-wave (CW) Tm:YAP slab laser operating at room temperature. Two fiber-coupled laser diodes were used as pump source, the maximum output power of 105 W at 1936.4 nm was achieved with the total incident pump power of 308 W, corresponding to the slope efficiency and optical-to-optical efficiency were 41.4% and 34.1% with respect to the incident pump power, respectively. At the maximum output power, the beam quality factors M2 were 2.76 and 2.78 in the x and y directions, respectively. Besides, a theoretical model was presented to predict the temperature distribution, thermal induced stress and laser performance of the Tm:YAP slab laser, and the experimental results were consistent with the theoretical simulation results which indicated that this model could simulate hundred-watt-level Tm:YAP lasers well.