A general Boundary Element methodology is developed to study two-dimensional steady-state viscoelastic circular contact problems. The methodology relies on an ad hoc defined steady-state viscoelastic Green's function, which accounts for the circular domain, typical, for example, of a mechanical pin joint, and can be employed to manage any real viscoelastic material, characterized by a continuum spectrum of relaxation times. The contact problem can be then easily formulated in the form of a spatial convolution product between surface stresses and displacement, which paves the way to solve contact problems of a countless number of engineering relevant systems, where multiple viscoelastic contacts occur. These include, inter alia , viscoelastic rolling element bearings, and pin joints. [ABSTRACT FROM AUTHOR]