In the context of Finite Element Analysis, the finite element equations are traditionally solved using Newton’s method to incrementally solve with respect to the degrees of freedom of the problem as the structure under consideration is subjected to prescribed ‘loading’ and boundary conditions. Due to its formulation however, Newton's method is not a good choice in cases where the stiffness matrix of the structure is not purely positive definite, obstructing the analysis of problems that exhibit instabilities in the form of softening, buckling and material failure.

The Arc Length Method, or also commonly called “The modified Riks method” is a powerful numerical technique for solving systems of nonlinear equations. Introduced as a geometric extension to the aforementioned Newton method, the Arc–Length method promises to solve highly nonlinear systems of equations efficiently and accurately even when the former fails.