The vehicle stability is a widely studied topic today, since it is responsible for a better understanding as it is one of the main vehicular accident rate problems in the world: the rollover accident. The main goal for researchers is to determine a way to predict vehicle behaviour under some circumstances. Davies method is a mathematical tool, which uses Screw theory and Graph theory together with Kirchhoff laws for build and to solve the static and kinematic analysis of any mechanism. This paper compares the classic vehicle stability analysis of a model in two dimensions, and the vehicle stability analysis of a threedimensional model using the proposed method.