In this study, the stress and deformation behavior characteristics of a flexible joint for a gas pipe have been analyzed by a finite element method. These characteristic results may investigate the strength safety analysis of a flexible joint, which is composed by a spiral corrugation pipe or a rectangular corrugation model and a plane pipe. The FEM computed results show that an optimized spiral corrugation pipe model is a inclined angle of $4.7^{circ}$ and a corrugation height of 1.5mm. And also, a rectangular corrugation pipe model of $90^{circ}$ is recommended in strength safety rather than a spiral corrugation pipe with an inclined angle. Thus, a corrugated pipe for an increased strength safety is to recommend a reduced pitch and curvature radius of an inclined corrugation.