Based on the Unified Strength Theory, a solution of the ultimate bearing capacity for strip foundations near slopes was derived by taking the comprehensive effects of intermediate principal stress, the horizontal distance of foundation base from the slope shoulder and the slope angle into account. Applicable conditions and calculation procedures of the obtained solution were provided, and differences from the ultimate bearing capacity equation of strip foundations on the level ground were discussed. Then, comparability analysis of the proposed solution was conducted, and the proposed solution was verified by comparing with results of the model test and the upper bound method available in the literature. Finally, the influence of each parameter was analyzed. It is found herein that the solution of ultimate bearing capacity in this study has good comparability, which can be degraded into the solution of Mohr-Coulomb strength criterion, and a series of solutions for new strength criteria could be obtained. Results of this study have a good agreement with that of the model test and the upper bound method, thus the correctness of the proposed solution is demonstrated. The intermediate principal stress has an obvious improvement effect on the ultimate bearing capacity of strip foundations near slopes, and the result without considering the intermediate principal stress effect tends to be conservative. The ultimate bearing capacity of strip foundations near slopes gradually increases with the increase of the horizontal distance of foundation base from the slope shoulder, and it is consistent with that of strip foundations on the level ground when the distance from the slope shoulder is equal to a critical value. Furthermore, the increase in the slope angle brings a remarkable reduction in the ultimate bearing capacity, and the reduction is more significant with the greater effect of intermediate principal stress. The result obtained in this study can provide a theoretical reference for optimization design of foundations near slopes.