To be able to reduce the size of products having electronic devices, it becomes more and more important to miniaturize the electro-mechanical parts of the system. The use of micro mechanical connectors and contact structures implies the need of methods for estimating the properties of such devices. This work will, by use of finite element modeling, treat the influence of a thin film constituting at least one of the contacting members of an electrical contact. The error introduced by using the traditional Maxwell/Holm contact constriction resistance theory will be investigated. Numerical methods are used to present a way to approximate the total resistance for the thin metal film contact.