•A unified solution for the stationary/nonstationary stochastic vibration problems of the composite laminated plate with thermal and aerodynamic loads is proposed.•The modified Fourier method combined with pseudo excitation method (PEM) is adopted to obtain the solutions for the cases with classical and elastic boundary conditions.•An experiment study concerning random vibration of the composite plate under acoustic loads is performed.•The effects of the boundary condition, thermal load, fiber orientation and aerodynamic pressure on the random vibration behaviors of the composite laminated plate in supersonic airflow are clearly figured out. This paper investigates the stationary/nonstationary stochastic responses of composite laminated plates under thermal and aerodynamic loads, where the point random excitation, distributed random excitation and base acceleration random excitation can be considered. The effects of the thermal stress and aerodynamic pressure are taken into account by employing the thermo-elastic theory and supersonic piston theory, respectively. The Hamilton's principle is used to formulate the governing equations of the system, and the solutions for the dynamic problems of cases having classical and non-classical (elastic) boundary conditions are obtained by the modified Fourier method combined with pseudo excitation method (PEM). To validate the proposed formulation, a sufficient number of numerical and experimental studies are conducted for the free vibration, flutter and stochastic response analysis of composite laminated plates with various boundary conditions. Satisfactory agreements are shown between the computed results and those from the finite element method (FEM), published literature and experiments. Finally, the effect of boundary condition, thermal load, fiber orientation and aerodynamic pressure on the random vibration behaviors of composite laminated plates is also presented. Display omitted