Analytical (closed-form) solutions are developed for the deflections and rotations of thick specially orthotropic plate twist specimens by using first-order shear deformation theory. Results are compared with outcomes from finite element method, previously reported experiments, and a classical laminated plate theory solution. A [(0/90)₆]_s cross-ply laminate and a sandwich panel with aluminum face sheets and a polyvinyl chloride (PVC) foam core are used as baseline materials. Overall, good agreement between first-order shear deformation theory and finite element method is obtained for compliance predictions. It is found that the proposed first-order shear deformation theory approach can be used to adequately calculate the deflections of specially orthotropic plates from low to moderately high side length to thickness ratios ( ≤ 20 ) . Examination of the in-plane shear modulus ratio between face sheets and core ( G 12 f / G 12 c ) points out that first-order shear deformation theory slightly underpredicts the compliance with respect to finite element method, specially for G 12 f / G 12 c ratios larger than 100. Both solutions based on plate theories are suitable to estimate the compliance of cross-ply laminates with moderate G 23 / G 12 ratios ( G 23 / G 12 ≤ 5 ). First-order shear deformation theory is able to properly predict the compliance of square and rectangular laminates with aspect ratios lower than 10. Good agreement between published compliance measurements and those predicted by first-order shear deformation theory is found for Maple plywoods, monolithic metals, and specially orthotropic sandwich panels.