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The nonlinear transient response of composite shell panels subjected to mechanical load in hygrothermal environments is investigated using finite element method. The present formulation considers doubly curved thick shells and includes large deformations with Green–Lagrange strains. The analysis is carried out using quadratic eight-noded isoparametric element. The nonlinear time dependent equation is solved by using the Newmark average acceleration method in conjunction with an incremental modified Newton–Raphson scheme. The validity of the model is demonstrated by comparing the present results with the solutions available in the literature. A parametric study is carried out varying the curvature ratios and side to thickness ratios of composite cylindrical, spherical and hyperbolic paraboloid shell panels with simply supported boundary conditions.