Constructions in the form of rectangular planar plates and shallow shells reinforced by a cross system of ribs of great rigidity and loaded with an arbitrary lateral load are considered. The stress-strain state of such structures is described by technical theories of plates and shallow shells. The effect of the stiffeners is taken into account in the equations as additional terms containing factors with the Dirac δ-function and its derivatives. The plate and the shell may have a stepwise variable thickness. The ribs are arbitrary thin-walled beams of variable cross-section that play an essential role in providing the load-carrying capacity of the structure as a whole. The stress-strain state of not only the plate and the shell but also the stiffeners themselves is determined. The questions of the rate of convergence of solutions in the form of trigonometric series describing the stress-strain state in the stiffeners are discussed. The results of analyses of reinforced plates are presented.