We consider a residually stressed plate-like body having the shape of a cylinder of cross-section and thickness h, subjected to a system of loads proportional to a positive multiplier . We look for the smallest value of the multiplier such that the plate buckles, the so-called critical multiplier. The critical multiplier is computed by minimizing a functional whose domain of definition is a collection of vector fields defined in the three-dimensional region = x (–h/2,+h/2). We let -> 0 and we show that if the residual stress and the incremental stress induced by the applied loads scale with in a suitable manner, then the critical multiplier converges to a limit that can be computed by minimizing a functional whose domain is a collection of scalar fields defined on the two-dimensional region . In the special case of null residual stress, the Euler–Lagrange equations associated to this functional coincide with the classical equations governing plate buckling.