The conical surface sealing performance of a pipe connection fit (PCF) has been studied by means of an equivalent mechanical model and the contact finite element analysis (FEA). By building an equivalent mechanical model, we studied the basic mechanical relations between the jointing parts, proposed a sealing mechanism, and identified a basic pretension-relaxation-leakage mode occurring in the sealing process of a conical surface PCF. Then we simulated the contact states of the PCF sealing surface using a multi-body elastic contact finite element method (FEM). In addition, the characteristics of the pretension-relaxation-leakage mode were further discussed in terms of the contact forces as well as the contact areas on the sealing surface. These results revealed some fundamental characteristics inherent in the sealing process of conical surface of PCFs, and demonstrated the potentials of the contact FEA in studying PCF sealing performance.