Abstract <p>Orthotropic shells are widely used today in industry and in engineering. For example, they are employed in inertial thermonuclear synthesis and also as containers for phase-transfer heat storage units. In view of their growing popularity, modeling of their stress–strain state is of great interest, especially in the presence of a crack. Existing theories of shells and transverse shear are unhelpful, since they are physically unrealistic: they permit interpenetration or overlap of the crack surfaces at the compressive edge under the action of a flexural load. On the basis of nonlinear continuum theory and perturbation techniques, however, the stress–strain state of an elastoplastic orthotropic shell along a curve with an internal crack may be modeled by means of singular integral equations, as established in the present work.</p>