In this paper, the results for the stress intensity factor of a mode III (tearing mode) have been investigated using the method of finite element analysis. A compact tension specimen containing a pre-crack and subjected to out-of-plane tearing loads has been used. A three-dimensional finite element analysis (FEA) model using the ANSYS program has been built for specimens made of different bio-medical materials such as stainless steel, titanium, alumina, high density polyethylene(HDPE) and polymethyl methacrylate(PMMA). Such materials are used for hip and knee replacement and for dental implants. The effects of notch angle, notch tip radius and pre-crack length on the stress intensity factor for the mode III have been studied. The model was extended to study the effect of crack and bonding line separation distance on stress intensity factors for specimens made of different homogeneous materials such as stainless steel bonding with epoxy as a filler material. The number of elements along the crack front and crack tip has been varied to determine its effects on the stress intensity factors. It is concluded that the pre-crack must be greater than or equal to 33% of the total crack lengt and the notch must be a blunt notch in order to obtain the stress intensity factor, K II I , independently, of the crack notch angle. However, the stress intensity factor is independent of the crack and bonding line separation distance when it is less than or equal to 15% of the specimen width. The results for the stress intensity factors, K II I , are obtained using a linear elastic fracture mechanics (LEFM) approach.