The pipe connection process using a clamping ring is used for joining small pipes in the refrigerator and air-conditioner industries instead of the brazing process, which induces inevitable thermal deformation in the pipes. However, few studies have been carried out on the process to select optimal parameters in joining pipes, and studies on the relation between the process parameters of the connection and connecting force of the joint have not been conducted. In this study, the connection process of pipes with the clamping ring was modeled using the finite element method (FEM) and analyzed to obtain the contact stress distribution between the pipes with which the connecting force of the joint was estimated. Considering the characteristics of pipe connection, the process was modeled and simulated in a two-dimensional axisymmetric solution domain. With the numerical model, the effect of ring shape on the connection was studied by adding a projection to the end of a ring or changing the length of a ring. The results of the analyses revealed that the contact stress distribution could be predicted with the suggested model. The effect of the ring shape was also presented. The effect of any combination of process parameters could be easily estimated through the related analyses.