A theoretical investigation of the buckling behavior of imperfect ring and stringer stiffened shells under axial compression was carried out. The nonlinear Donnell-type equations for imperfect shells with "smeared out" ring and stringer stiffeners have been reduced to an equivalent set of nonlinear ordinary differential equations. The resulting two-point boundary value problem was solved numerically by the "shooting method." The use of this method made it possible to investigate how the axial load level at the limit point is affected by the following factors: the prebuckling growth caused by the edge constraint, different sets of boundary conditions, the orientation and shape of the axisymmetric and asymmetric imperfection components and the eccentricity in the load application. As a result of this investigation, a simple formula is proposed which makes it possible to take into account both the effect of initial imperfections and the effect of the appropriate boundary conditions.