This paper aims to present the critical top tension for static equilibrium configurations of a steel catenary riser (SCR) by using the finite element method. The critical top tension is the minimum top tension that can maintain the equilibrium of the SCR. If the top tension is smaller than the critical value, the equilibrium of the SCR does not exist. If the top tension is larger than the critical value, there are two possible equilibrium configurations. These two configurations exhibit the nonlinear large displacement. The configuration with the smaller displacement is stable, while the one with larger displacement is unstable. The numerical results show that the increases in the riser’s vertical distances, horizontal offsets, riser’s weights, internal flow velocities, and current velocities increase the critical top tensions of the SCR. In addition, the parametric studies are also performed in order to investigate the limit states for the analysis and design of the SCR.