This work deals with investigation of the interface between unidirectional E-glass fiber and epoxy matrix composites. The two parts in this work are: 1. A periodically constrained finite element (FE) model built as a Representative Volume Element (RVE). 2. A second FE model to predict the shear properties of the interface of the composite. The first model was built to examine validity of cohesive zone elements of the FE package. Properties of the interface were incorporated into the second model with the help of experimental pull-out test results. A parametric study of the cohesive zone was conducted by variation of its characteristics in the second part. The load carrying capacity of a composite material is based on its ability to transfer the stress between its components. The results of this study yielded findings about stress patterns of the interface responsible for the load transfer from the fiber to the matrix.