The flow behavior of Ti2041 alloy was studied through hot compressive experiments. The constitutive model of alloy established by back propagation (BP) neural network has high accuracy, which correlation coefficient reached 0.99613, the average relative error is 4.498%, the predictive value of deviation within 10% data points up to 92.98%. Based on the experimental data, the strain rate sensitivity, the power dissipation and the instability parameter were investigated. Processing maps were established. Through processing map prediction and microstructure observation, the instability zones are mainly flow localization(650~775℃/0.056~1s-1) and mechanical instability (825~900℃/0.056~1s-1), and the deformation mechanism of the stability zone is mainly dynamic recrystallization. It is found that the optimal deformation parameters are that: deformation temperature760~825℃/825~900℃, strain rate 0.001~0.01s-1 /0.0032~ 0.056s-1.