The dynamic instability analysis of delaminated composite structures subjected to in-plane pulsating forces is carried out based on the higher order shell theory of Sanders. In the finite element (FE) formulation, the seven degrees of freedom per each node are used with transformations in order to fit the displacement continuity conditions at the delamination region. The boundaries of the instability regions are determined using the method proposed by Bolotin. The numerical results obtained for skew plates and shells are in good agreement with those reported by other investigators. The new results for delaminated skew plate and shell structures in this study mainly show the effect of the interactions between the radius-length ratio and other various parameters, for example, skew angles, delamination size, the fiber angle of layer and location of delamination in the layer direction. The effect of the magnitude of the periodic in-plane load on the instability regions is also investigated.