Abstract: The tubular column of drilling and screw pumps is subjected to both the axial pressure and torque loads in operations. Slow dynamic method is proposed to calculate the column buckling torque and pressure. Based on the idea of the transient dynamics method in solving the statics problem, the loading, and the strategies of choosing the damping factor and sub-steps are analyzed. The numerical results show that when the axial pressure and torque are acted alone or simultaneously, the finite element solution is in good agreement with the analytical solution. This paper also analyzes the influencing factors of the computational effciency of the slow dynamic method.