Contact characteristics of friction pair play a crucial role in the torque transmission capacity and temperature rise prediction of automotive clutches. In this study, a Multi-cone friction pair used in wet clutches has been proposed. Each pair of conical contact is considered as the contact between a finite stiffness punch and an elastic half-plane, and 2D finite element (FE) models are developed to calculate the contact load assignments. Considering the capsizing moment and stress singularity at the end of the contact interface, an analytic model is established to obtain the contact pressure distribution on each conical contact interface based on the results of contact load assignments. Finally, the numerical examples are given, and the influences of axial load, mating material characteristics, friction coefficient, and cone angle on contact pressure distribution have been discussed in detail, which supplies the guidance of parameters design for Multi-cone friction pair.