Abstract: Based on the characteristic of mechanism mode in large deformation, this paper proposes a method for determining whether a geometrically unstable system of a single degree of freedom is constantly unstable or instantaneously unstable, and in the former case the paper further proposes a bi-element construction method to build the mechanism mode in large deformation. The method is nearly as simple as solving a quadratic equation without the need for solving transcendental equations and moreover the method can give complete solutions for modes, solution paths, limit points and bifurcation points. The method is found to be intuitive in theory, simple in formulation and complete in solutions. The method can be used as a supplement or extension to analysis of geometrical stability in structural mechanics course.