This study is an attempt to modeling a frictional gap in a crack closure process under compressive loading conditions in which the crack surfaces are in touch and the effects of friction between them are significant. An iterative finite element (FE) solution is developed to model a finite crack in an interfacial layer with varying material properties. A mere application of a Lagrange multiplier formulation (node-to-node, NTN, or node-to-segment, NTS) in a developed FE framework to fulfill the contact constraints between contacting surfaces is discussed which improves the penalty formulation used in ANSYS. We then argue that the penalty formulation allows for a certain amount of crack surface interpenetration whereas the Lagrange multiplier formulation fulfils the contact constraints more accurately. This technique is easy to implement and offers higher accuracy than the equivalent FE solution, available in commercial FE software such as ANSYS 9.0, to the same system.