To joint a dam with resistant mountain rock is a common measure against sliding. Due to complicated forces in this case, finite element method is usually adopted in the safety evaluation. In this research, we applied mechanics of material to analyse the forces between the dam and the downstream mountain rock mass. Moreover, we put forward a simplified method of calculating the slide-resistant stability of dam foundation and deduced the formula based on rigid-body limit equilibrium solution for gravity dam foundation. By comparing it with finite element method, we conclude that the basic assumption of the present method based on material mechanics is reasonable. Furthermore we applied this method to the calculation of a typical calculation example and an engineering example. Results show that as for the engineering example, the anti-sliding safety factor is 4.87 and 2.97 respectively in the presence and in the absence of mountain rock resistance under normal working condition, and 3.89 and 2.24 under seismic condition. The safety factors in both conditions are greatly improved in the presence of mountain rock resistance. As a preliminary exploration on dam foundation with complex forces, the method has clear physical and mechanical meaning, and convenient calculation process.