There exists a structural problem for link structures in the unstable state. The primary characteristics of this problem are in the existence of rigid body displacements without strain, and in the possibility of the introduction of prestressing to change an unstable state into a stable state. When we make local linearized incremental equations in order to obtain knowledge about these unstable structures, the determinant of the coefficient matrices is zero, so that we face a numerically unstable situation. This is similar to the situation in the stability problem. To avoid such a difficult situation, in this paper a simple and straightforward method was presented by means of the generalized inverse for the numerical analysis of stability problem.