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In this article, the geometrical nonlinear free vibration behaviour of shear deformable laminated composite single/doubly curved shell panel in hygrothermal environment is investigated. A general nonlinear mathematical model of laminated composite doubly curved shallow shell panel has been developed based on the higher order shear deformation theory and Green-Lagrange geometric nonlinear kinematics. All the nonlinear higher order terms have been included in the present mathematical model to achieve a realistic case. In addition to that, the composite material properties are considered as temperature and moisture dependent through hygro-thermo-elastic constitutive relations. The governing equation of laminated composite curved panel is obtained using Hamilton’s principle and discretised using nonlinear finite element steps. The desired responses are computed numerically using a direct iterative method. The convergence behaviour of present numerical model has been checked and validated by comparing the responses with those available published results. The effect of different geometrical and/or material parameters on nonlinear vibration behaviour of laminated composite doubly curved shell panel under hygrothermal environment is computed and discussed in detail. [ABSTRACT FROM AUTHOR]