V-Coupling is used as a mechanical fastener to connect the turbine housing and the bearing housing in a turbocharger. The back plate is located between the turbine housing and the bearing housing, which is compressed by the bolt clamping force of coupling to prevent gas leakage under turbocharger operation. This paper presents the theoretical and analytical methods to predict the sealing performance by calculating the contact pressures on the back plate. The mathematical model was constructed to derive the contact force on the back plate by considering the force transfer mechanism. And, finite element analysis was carried out to predict the contact pressures by applying the bolt load in the coupling system. As a result, the analysis results of the mathematical model are well consistent with the results of the finite element analysis. Therefore, in the early design stage of turbocharger coupling, mathematical model would be helpful to determine the design parameters.