The dual-axis buckling of Laminated composite skew hyperbolic paraboloid with cutouts subjected to the in-plane biaxial and the shear load is investigated for various boundary conditions using the present mathematical model. Variation of transverse shear stresses is represented by a second-order function across the thickness, and the cross-curvature effect is also included via strain relations. The transverse shear stress-free condition at the shell top and bottom surfaces is also satisfied. This mathematical model (having a realistic second-order distribution of transverse shear strains across the thickness of shell) requires unknown parameters only at the reference plane. For generality in the present analysis, nine-node curved isoparametric element is used. So far, no solution exists in the literature for dual-axis buckling problem of laminated composite skew hyperbolic paraboloids with cutouts. As no result is available for the present problem, the present model is compared with suitable published results and then it is extended to analyze biaxial and shear buckling of laminated composite skew hyperbolic paraboloids. A C-0 finite element coding in FORTRAN is developed to generate many new results for different boundary conditions, skew angles, lamination schemes, etc.