Taking the jointed rock slope as the research object, the multi-objectives of safety and economy nonlinear mathematical programming model of rock slope anchorage is established based on the extreme value theory of plastic mechanics. This model uses safety coefficient of the sliding surface and the anchor cost as the objective functions, and the direction of the anchoring force, the length of the anchors, the shearing force and normal force of the structural plane as the decision variables. It combines the equilibrium equation constraint of the rock blocks, the yield condition of the structural plane and the additional constraints of the anchors. According to this model, the safety coefficient, optimal anchor cost and optimal anchoring angle are obtained using the linear weighted sum method. This method has the merits of clear concept and high calculation accuracy.