Abstract: The asymmetric failure modes involving the slope face failure and the below-toe failure are proposed, and then new solutions of Meyerhof's bearing capacity for strip foundations near slopes are presented by adopting the shear strength equation of unified strength theory under plane strain conditions. The combined effects of the intermediate principal stress, the horizontal distance of foundation from the slope shoulder, the slope height and the base roughness are taken into account. The specific application steps of the obtained solutions are provided, and theoretical degradation analysis and comparison verifications are conducted. It is found herein that the proposed asymmetrical failure mode considering the contribution of soil strength behind the slope is more consistent with the actual failure behavior of foundations near slopes. The obtained solutions of Meyerhof's bearing capacity for foundations near slopes are in good agreement with those of the model tests and numerical simulations in the literature. The intermediate principal stress has a marked 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 the 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 side, which is of theoretical guiding significance to the optimal design of foundations near slopes.