This paper investigates a reliable design approach for reinforced concrete panels subjected to the combined action of in-plane shear and out-of-plane bending moments, which develop in webs of boxgirder bridges and similar structures. Neglecting this interaction is not consistent with the actual structural behaviour at failure and can potentially lead to an insufficient design. Existing design approaches (based on the rigid-plastic stress field (RPSF) method) account for this interaction by reducing the shear strength as a function of the transverse moment and predict a substantial reduction of the shear strength. The proposed multi-layered elastic-plastic stress field (ML-EPSF) approach represents an equilibrium solution (satisfying the static and kinematic theorem of the theory of plasticity) with larger shear strength, especially in presence of small transverse moments. The ML-EPSF model confirms the basic principle of the RPSF interaction models, but shows that its underlying hypotheses are however very conservative and might need some adjustments.