This thesis presents a reliability analysis of shallow strip footings resting on a soil or a rock mass and subjected to a central (vertical or an inclined) load. The deterministic models used are based on limit analysis failure mechanisms and on numerical simulations using FLAC 3D. The variability of the soil and the rock properties and that of the applied footing load are modeled as random variables. The reliability of the foundation is determined using Hasofer-Lind reliability index. The failure probability is computed using RSM and SRSM methods. It was shown that, in the case of a soil mass (where the system response adopted in the analysis is the safety factor Fs defined with respect to soil parameters c and tano), the negative correlation between c and cp increases the reliability of the foundation. The use of Fs allows one to (i) determine the zones of predominance of footing sliding and soil punching in the interaction diagram for different types of soil and/or footing loads uncertainties and (ii) rigorously compute the failure probability for a given configuration of (V, H). The variability of Fs is more significant in the zone of footing sliding predominance where it largely depends on the variability of H. In contrast, this variability of Fs depends on the variability of in the zone of soil punching predominance. In the case of a rock mass (where the system response adopted in the analysis is the ultimate bearing capacity qu), it was found that the variability of qu is very sensitive to the rock parameters GSI (Geological Strength Index) and c (Uniaxial compressive strength of the intact rock material), and becomes less important when these parameters are negatively correlated. For design, an iterative procedure is performed to determine the breadth of the footing for a target reliability index