Abstract: Under the deep well, extra- deep well, extend well and horizontal well, the properties of the leakage and jumped - out of the casing connector is the topic that is studied forever at home and abroad in the research of the oil-gas pipeline mechanics. Based on the study of many literatures, the develop object of the premium connections was presented in the paper, the mechanism of the leakage and jumped-out of the threads of casing connection was discussed in detail. The stresses of the connection of the buttress and round threads were analyzed with finite element method (FEM), the curves of the jumped-out loads varied with the time was obtained when the flank angles of the buttress are 3°, 5° and 10° degreed, respectively. With the three tapers 1/14, 1/16 and 1/17, for the round casing connector, the curves that the jump-out loads varied with the loading process were obtained. It provides the theoretical supports for the selection of the casing connectors in the extra-deep well and complex well.