Abstract: A physical-mechanical model of casing connetion joints was bulit for the premium thread and then the axial deformation of a single thread tooth was analyzed. According to the deformation compatibility equation of meshing thread teeth, a set of equations for calculating the contact stress of the casing thread were deduced. Then the inhomogeneous stress distribution of the casing thread was obtained. The reference of the analytic method for connection capability analysis was verified by finite element calculation results. Combining the elasticity theory and the calculation criterion of the API buttress thread, the limit state equations of non-API casing connection's failure modes were derived from the reliability theory. The random sampling of thread processing parameters was carried out with the Monte Carlo method, and then the failure probability and its corresponding reliability were obtained by statistics. The calculation results show that the failure modes' reliability values of non-API casing connection should be ordered below:thread thread slipping > pipe yield > shear failure > joint rupture.