The purpose of this work is to present some numerical results on nonlinear, snap-through buckling of shallow spherical shells made of laminated composite materials under general static loading. Isotropic shells are covered as a special case of the general problem. A special-purpose finite-difference computer program has been developed. Moreover, the general-purpose computer program ANSYS has also been used. Effects of various material properties on the nonlinear behavior of the shells are investigated. One of the conclusions of the study is that ANSYS may yield erroneous results in some cases. Another conclusion is that the buckling curves of composite shallow spherical shells have a shape similar to that of the corresponding isotropic shell. This finding implies that the geometry of a shell may be an important factor in giving a characteristic shape to the buckling curve, at least for the shell parameters considered here.