The time-dependent deflection values of the flat/curved hybrid fibre (Glass–Carbon–Kevlar)-reinforced composite panels under the influence of the mechanical loading (UDL and SDL) and the elevated thermal environment are analyzed in this research. To compute the numerical responses, a higher-order kinematic model is prepared considering the effect of single/double curvature of the shell panel. The weak form of the governing equation is established through the variational technique. The steady-state deflections are obtained by solving the discrete form of governing equation of transient vibrations using finite element method (FEM) by employing Newmark’s time integration method in MATLAB environment. The isoparametric Lagrangian element (nine-noded) is adopted to discretize the system equation of the hybrid panels. The validity of the numerical solutions, computed using the experimental hybrid composite properties, is verified with the experimental (in-house) results as well as with the benchmark results available in the published literature. Finally, the parametric study of dynamic deflection characteristics of hybrid composite shallow shell panels is carried out by varying the parameters such as curvature ratio, support conditions, hybrid schemes and type of loading in the elevated thermal environment and the results are discussed in detail.