The finite element model of various laminated composite structures with delamination is developed based on the higher-order shear deformation theory. In the finite element formulation for the delamination, 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 numerical results obtained for various composite plates and shells with delaminations are in good agreement with those of other preceding investigations. The new results for laminated structures in this study mainly show the effect of the interactions between the geometries and other various parameters, for example, delamination size, the number of layer and location of delamination in the layer direction. Key observation points are discussed and a brief design guideline is given.