The degenerate shell element is considered for the geometrically nonlinear finite element analysis of shells. Total Lagrangian formulation is used for describing the nonlinear responses. To overcome the locking phenomenon of the degenerate shell element(9 node Heterosis element), selectively reduced integration technique(bending stiffness-$3{ imes}3$ rule, shear stiffness-$2{ imes}2$ rule, membrane stiffness-$2{ imes}2$ rule) is introduced. This element exhibits good performance even for thin shells. The Arc-length method, in combination with the modified Newton-Raphson technique, has been applied for finding limit points and tracing the post-critical responses(snap-through and snap-back problems). Numerical examples are solved to assess the performance of the degenerate shell element under geometrically nonlinear conditions including post-critical behaviors.