Jointed rock mass is inherently heterogeneous because of the presence of discontinuities. The discontinuities may occur in the form of joints, faults, and fissures. The variability of engineering properties of jointed rock mass depends on geometrical shapes due to past geological processes. The spatial arrangement, surface roughness, number, length, orientation, and inter-connectivity of discontinuities may play a significant role in an accurate prediction of jointed rock mass strength. The jointed rock mass strength is pivotal for the safe and economical design of strip foundations in rock engineering. The reliability method used in this work provides a more rational approach over the conventional factor of safety approach by accounting for the variability of properties of the jointed rock mass. A reliability based optimization of foundations built on jointed rocks with two discontinuity sets is presented to compute the optimum value of the allowable bearing capacity of strip footings. The discontinuity strength model along with the modified Bell approach is adopted to determine the ultimate bearing capacity. Reliability analysis is conducted by treating uniaxial compressive strength of intact rock, discontinuity cohesion, discontinuity orientation, joint spacing, rock material frictional angle, and discontinuity frictional angle as random variables. The effects of orientation on the allowable bearing capacity are presented for the target probability of failure of 0.13%. © ASCE.