The research work presented in this paper refers to a new slope stability analysis method used for landslide risk evaluations. It is an extension of the 3-dimensional upper-bound slope stability analysis method proposed by Chen et al. in 2001,which employs the Mohr-Coulomb’s associative flow rule. It has been found that in a 3-dimensional area,a prism may not be able to move at friction angles to all its surrounding interfaces,as required by this associative rule,and convergence problems may occasionally arise. The new method establishes two velocity fields:(i) The plastic one that represents a non-associative and the best representative dilation behavior,and (ii) the virtual one that permits the solution for factor of safety in the work and energy balance equation. The new method can then allow any input value of dilation angle and thus solve the convergence problem. A practical application to a concrete dam foundation is illustrated. The research work presented in this paper refers to a new slope stability analysis method used for landslide risk evaluations. It is an extension of the 3-dimensional upper-bound slope stability analysis method proposed by Chen et al. In 2001, which employs the Mohr It has been found that in a 3-dimensional area, a prism may not be able to move at the friction angles to all its surrounding interfaces, as required by this associative rule, and convergence problems may occasionally arise. The new method established two velocity fields: (i) The plastic one that represents a non-associative and the best representative dilation behavior, and (ii) the virtual one that permits the solution for factor of safety in the work and energy balance equation. new method can then allow any input value of dilation angle and thus solve the convergence problem. A practical application to a concrete dam foundation is illustrated.