Applications of skew plates in the practical civil engineering are well-established. A look into the papers about the failure of laminated composite structural elements revealed that composite skew plates have not been studied for failure in detail. The first-ply failure load and frequency reduction due to such a failure are reported considering practical parametric variations of composite skew plates. Different well-established failure criteria, including the most recent Puck failure criterion, are used to investigate the first-ply failure response by the finite-element method. The results obtained are postprocessed to formulate specific recommendations regarding the relative behavior of different skew plate combinations in terms of the first-ply failure.