In this analysis, the effect of an imperfect interface on the stress singularity of an orthotropic elastic bimaterial wedge subjected to traction free boundary conditions, is investigated, where the planes of symmetry are aligned, and one symmetry plane is along the interface and another symmetry plane coincides with the cross-sectional plane. The Stroh formalism with the method of separation of variables are used to obtain the relevant expressions for displacements and stresses. At the interface, only the interfacial tractions and the displacement normal to the interface are assumed to be continuous. The imperfect bond is modeled using a local coordinate system, where each tangential traction component in this local coordinate system is directly proportional to the corresponding displacement discontinuity and inversely proportional to the distance from the wedge apex. The order of singularity is computed numerically for graphite/epoxy wedges and presented for various imperfect interface conditions. The numerical results agree with the available results for the fully bonded case. It is expected that when the axes of local and global coordinate systems are aligned, that the in-plane and antiplane problems are uncoupled, and this feature also can be seen in the numerical results.