A buckling analysis is presented for a circular cylindrical shell subjected to nonuniform external pressure. The general approach is not restricted with respect to the distribution of the lateral pressure. However, the final formulation is specialized for the case in which the pressure distribution is of the form p = p0 + p1 cos φ within a centrally located circumferential band. In the buckling analysis the stability criterion is based on the principle of minimum potential energy, and the Rayleigh-Ritz procedure is used to expand the displacement components in trigonometric series. Buckling pressures are computed in terms of nondimensional parameters and are presented in graphical form.