This study investigates the uncertainty related to the influence of the variability of the soil-structure interaction (SSI) properties on the transmission of ground movements to structures. These movements can be produced by tunnels excavation, sinkholes, mining subsidence, etc. This article aims to quantify the relative importance of the variability of every SSI parameter on the structure response via a sensitivity analysis (SA). An analytical approach is applied where the structure is modeled by an elastic Euler-Bernoulli beam and the soil by a combination of elastic springs as per the Winkler model. The target of the analytical approach is to propagate the parameters variability (namely the building stiffness EI, the soil modulus KB and the structure length L) which are assumed to be of a random nature. To avoid time and computation difficulties, a meta-model that reflects the structure response is developed. Based on this meta-model, the SA is performed using three selected procedures, one local and two global, namely, one-way analysis, Sobol and McKay respectively. The contribution of each input parameter on the variability of the response in the domain of variation is then investigated using various sampling techniques, such as random Monte-Carlo Simulations (MCS) and the Latin Hypercube Sampling (LHS). After evaluating the sensitivities of the SSI parameters, confidence intervals are set and can be used by engineers and designers when evaluating the transmission of ground movements to structures when considering these uncertainties.