Conventional stability analysis of slopes is established on vertical slices with a linear Mohr-Coulomb (MC) failure criterion. In this paper, the soil mass of slopes is assumed to follow linear and nonlinear failure criteria. A new procedure is proposed for determination of stability factors of slopes using triangular slices within the framework of limit analysis method under plane strain condition. The potential sliding mass is divided into a series of triangular slices, rather than vertical slices as usual. Using a generalized tangential technique, the nonlinear failure criterion is simplified as a set of straight lines according to the linear MC failure criterion. The straight line is tangential to the curve of the nonlinear failure criterion. With a linear MC failure criterion, solutions to stability factors are determined by limit analysis theory, which agree well with the published solutions. With triangular slices method, a study is carried out to investigate the influences of nonlinear parameter on stability of the soil slope.