Slender shell structures described by ruled surfaces have been frequently used in civil engineering and, among these slender shells, conoidal shells are frequently favored as roofing units to cover large column-free areas due to their ease of construction, aesthetic value and structural efficiency. This work studies the nonlinear post-buckling behavior of a conoidal shell, using commercial finite element software ABAQUS®. The problem is geometrically nonlinear due to the shell strong geometric nonlinearity, especially in the case of shallow shells used in practical applications where quadratic nonlinearities play an important role. A detailed parametric analysis is conducted to show the influence of the shell geometry on the buckling loads and natural frequencies and, especially, on the nonlinear post-buckling behavior and stability.