Fracture behavior and pipe strength are very important to the integrity of energy plants, ocean structures, and so forth. The pipes of energy plants and ocean structures are subject to local wall thinning, resulting from severe erosion-corrosion damage. Recently, the effects of local wall thinning on fracture strength and fracture behavior of piping systems have been the focus of many studies. In this paper, the elasto-plastic analysis is performed by FE code ANSYS on straight pipes with wall thinning. We evaluated the failure mode, fracture strength and fracture behavior, using FE analysis. Also, the effect of the axial strain on deformations and failure modes was estimated by FE analysis.