In this paper, mechanical behaviors of the Elbow and Tee fittings connected to pipes by screw threads under internal pressure, external tensile loads and bending moment are analyzed using the Finite Element Method (FEM). FEM code employed is MARC. The maximum Mises stress of the Elbow and Tee fittings are obtained when the wall thickness is changed while the internal working maximum pressure is held constant at 20bar. The elasto-plastic stress states of screw threads the fittings and the pipes are obtained under internal pressure and external loads. Under the assumptions that nodal points are released when the strain of the elements reaches the rupture strain of the fitting’s material, the load when the rupture occurs at the screw thread is analyzed. The safety factor for the wall thickness of the Elbow and Tee fittings used in the experiment is found to be about 5. The results indicate deduced that the dimensions of Elbow and Tee fittings can be reduced. The strength of the fittings under internal pressure and external loads is obtained. It is found that the stress concentrates at the first root of male thread and expected that a fracture initiates at the first root. The strain of the Elbow and Tee fittings subjected to internal pressure were measured by using strain gauges. The numerical results are in a fairly good agreement with the experimental results.