A new Newton homotopy based method is presented that is able to determine robustly all the stationary points for the tangent plane distance function (TPDF). The solving method is equipped with the features of homotopy parameter and variables bounding that together result in a continuous homotopy path. All the stationary points of TPDF can be approached on one path, assuming only that the temperature, pressure, and composition of the component system are known. The performance of the method is examined with various LLE cases gathered from literature. The liquid phase behavior is described with NRTL and UNIQUAC excess Gibbs energy models. The consistency of stationary points is verified with the topological criterion. Based on this consideration, the proposed modified Newton homotopy method is found to be a robust computational tool for solving phase stability problems. (C) 2012 Elsevier Ltd. All rights reserved.