This paper proposes a kinematic model for sandwich plates and shells, utilising a novel zigzag function that is effective for symmetric and asymmetric cross-sections, and employing a piecewise through-thickness distribution of the transverse shear strain. The proposed model is extended to large displacement analysis using a co-rotational framework, where a 2D local shell system is proposed for the direct coupling of additional zigzag parameters. A 9-noded co-rotational shell element is developed based on the proposed approach, which utilises the MITC method for overcoming locking effects. Several linear/nonlinear analysis examples of sandwich structures demonstrate the effectiveness of the proposed approach.