Equivalent plate modeling techniques based on Ritz analysis with simple polynomials proved to be efficient tools for structural modeling of wings in the preliminary design stage. This paper describes a formulation of wing equivalent plate modeling in which it is simple to obtain analytic, explicit expressions for terms of the stiffness and geometric stiffness matrices without the need to perform numerical integration. The explicit expressions for the terms of the stiffness and geometric stiffness matrices are used for the buckling analysis of trapezoidal fiber composite wing skin panels. The formulation based on Ritz analysis using simple polynomials leads to explicit (axpressions for the analytic sensitivities of the stiffness and geometric stiffness matrices with respect to layer thickness, fiber orientations, and panel shape. Integration of the resulting buckling analysis based on the equivalent plate approach is discussed. To assess the new capability, test cases were chosen to address the convergence rate with increased polynomial order, the accuracy of analysis results for panels of general shape and the integration of wing box structural analysis with panel buckling analysis for fast structural analysis of airplane wings.