Geotechnical uncertainties may play crucial role in response prediction of a structure with substantial soil-foundation-structure-interaction (SFSI) effects. Since the behavior of a soil-foundation system may significantly alter the response of the structure supported by it, and consequently several design decisions, it is extremely important to identify and characterize the relevant parameters. Moreover, the modeling approach and the parameters required for the modeling are also critically important for the response prediction. The present work intends to investigate the effect of soil and model parameter uncertainty on the response of shallow foundation-structure systems resting on dry dense sand. The SFSI is modeled using a beam-on-nonlinear-winkler-foundation (BNWF) concept, where soil beneath the foundation is assumed to be an assembly of discrete, nonlinear elements composed of springs, dashpots and gap elements. The sensitivity of both soil and model input parameters on shallow foundation responses are investigated using first-order second-moment (FOSM) analysis and Monte Carlo simulation through Latin hypercube sampling technique. It has been observed that the degree of accuracy in predicting the responses of the shallow foundation is highly sensitive soil parameters, such as friction angle, Poisson’s ratio and shear modulus, rather than model parameters, such as stiffness intensity ratio and spring spacing; indicating the importance of proper characterization of soil parameters for reliable soil-foundation response analysis.