The nonlinear response of shallow shells subjected to combined acoustic and thermal loads is analyzed using an efficient nonlinear modal finite element (FE) formulation. The acoustic loads have non-Gaussian probabilistic characteristics and are simulated by an algorithm capable of reliably converging to a target power spectral density (PSD) function and marginal probability density function (PDF). Factors contributing to the panel structural stiffness, softening and hardening effects, and modal contribution are also investigated along with their impact on the root-mean-square responses. The Palmgren–Miner cumulative damage theory in combination with the rainflow counting (RFC) cycles methods was used to estimate the panel fatigue life. Parametric studies for cylindrical and spherical curved panels considering stacking laminations, radii of curvatures, acoustic and thermal loads are studied in detail.