In this paper, a probabilistic analysis is presented to compute the ultimate bearing capacity of a strip footing resting on a spatially varying rock mass. The rock is assumed to follow the generalized Hoek-Brown failure criterion. The uniaxial compressive strength of the intact rock (σc) was considered as a random field and the Geological Strength Index (GSI) was modeled as a random variable. The deterministic model was based on numerical simulations. The uncertainty propagation methodology employed in the analysis makes use of a non-intrusive approach to build up a sparse polynomial chaos expansion for the system response. The probabilistic numerical results were presented in the case of a weightless rock mass. The variability of the ultimate bearing capacity was found to decrease with the decrease in the autocorrelation distance. Sobol indices have shown that for the very large values of the autocorrelation distance, the variability of the ultimate bearing capacity is mainly due to σc; however, in the case of very small values of the autocorrelation distance, GSI is the most weighed variable.