Abstract: Asymmetric failure modes involving the slope face failure and the below-toe failure were proposed, and then new solutions of Meyerhof’s bearing capacity for strip foundations near slopes were presented by adopting the shear strength equation of Unified Strength Theory under plane strain conditions. Combined effects of the intermediate principal stress, the horizontal distance of foundation from the slope shoulder, the slope height and the base roughness were taken into account. Specific application steps of the obtained solution were provided, and theoretical degradation analysis and comparison verifications were conducted. It is found herein that the proposed asymmetrical failure mode considering soil strength contribution behind the slope is more consistent with the actual failure behavior of foundations near slopes. The obtained Meyerhof’s bearing capacity solution of foundations near slopes is in good agreement with that of model tests and numerical simulations in the literature. The intermediate principal stress has a markedly improvement effect on the bearing capacity of foundations near slopes. The bearing capacity of foundations near slopes first decreases and then remains unchanged with the increase of slope height. This study accounts for practical engineering conditions, such as the intermediate principal stress effect of soil strength, the asymmetry of failure modes, and soil strength at foundation lateral, which has theoretical guiding significance to optimal designs of foundations near slopes.