This paper quantifies the influence of uncertainty in the low-velocity impact responses of sandwich plates with composite face sheets considering the effects of obliqueness in impact angle and twist in the plate geometry. The stochastic impact analysis is conducted by using finite element (FE) modelling based on an eight nodded isoparametric quadratic plate bending element coupled with multivariate adaptive regression spline (MARS) in order to achieve computational efficiency. The modified Hertzian contact law is employed to model contact force and other impact parameters. Newmark's time integration scheme is used to solve the time-dependent equations. Comprehensive deterministic as well as probabilistic results are presented by considering the effects of location of impact, ply orientation angle, impactor velocity, impact angle, face-sheet material property, twist angle, plate thickness and mass of impactor. The relative importance of various input parameters is determined by conducting a sensitivity analysis. The results presented in this paper reveal that the impact responses of sandwich plates are significantly affected by the effect of source-uncertainty that in turn establishes the importance of adopting an inclusive stochastic design approach for impact modelling in sandwich plates.