The paper presents an analysis of the variation of stresses at a gas pipeline in a geometric discontinuity zone of the diameter. The analysis was performed by assimilating the pipe area with variable diameter with an axially symmetric structure loaded with internal pressure. Stresses were determined using the method of moments, theory for axially symmetrical structures. The analysis was performed according to a set of parameters that define the geometry of a joining between a conical frustum and a cylinder and the loading mode with internal pressure. Efforts and stresses were determined in the meridian direction and in the circumferential direction adjacent coatings combining the two axially symmetries.