 This paper proposes a computational algorithm which utilizes high performance computing resources to solve non-linear problems of continuum mechanics using finite element methods, fem. It is suitable for both static and dynamic problems, and can be applied to estimate the lifetime of structures when the load is defined by a load spectrum. The algorithm is particularly useful for non-linear problems, such as those involving contact between bodies, since it allows for quick and efficient evaluation of the results from the fem analysis. The algorithm was tested on two example problems, one involving contact between bodies and another involving a non-linear spring. The results were compared with analytical solutions and found to be accurate. This article was authored by Marion Handrich, Milan Vasco, Peter Capus, and others.