The Stokesian motion of viscous liquid lubricants in externally pressurized thrust collar bearings due to an off-centre pressure source has been studied by potential theory. The complex potential function that satisfies the boundary conditions of the bearing has been constructed by reflection across the ring circles. It has been determined in terms of Jacobi Theta Functions. The pressure distribution has been obtained for the following cases:-
i- Externally pressurized thrust circular concentric collar bearings.
ii- Externally pressurized thrust elliptic collar bearings.