The scope of this study is to examine a pressure sensitive yield criterion obtained from the literature and to implement this criterion due to the fully implicit backward Euler algorithm into a commercial finite element code via an appropriate user-subroutine under the consideration of small strains. The presented algorithm is then exemplarily employed to an adhesive layer of a three-dimensional single lap joint and the results are compared with the classical von Mises yield criterion. In addition, the stress distributions in the pure elastic and elaso-plastic range are compared.