A method is proposed to calculate Flexibility Factors for molded and mitered 90 deg polyethylene elbows for both in-plane and out-of-plane loading based on Code Case N-319-3, January 17, 2000. Displacement measurements in the direction of the applied forces were made during the testing of each elbow in addition to measuring the applied forces. By making use of Code Case equations, Flexibility Factors can be directly developed. Appendices to the paper show how these factors can be added to the deformation and rotation equation from curved Euler beam theory. One of the basic assumptions used in the Code Case and in this derivation is that there is no ovalization from torsion. Thus, the Flexibility Factor for the torsional displacement (twisting) of an elbow is one. Results show that an exact solution for Flexibility Factors based on the definition in Section III of the ASME Boiler and Pressure Vessel Code can be obtained for in-plane loading. However, for out-of-plane loading, the Flexibility Factors are geometry dependent if the values are based on measured elbow deflections. The difference is associated with the contributions of both torsion and bending to elbow deflections.