The problem of forced lobar vibrations of three layered cylinders of infinite extent subjected to boundary stresses which do not vary along the axis is considered. Linear viscoelastic theory is employed and the lobar vibrations of a thick single cylinder is accurately formulated. The solution to the three constrained layer cylinders is developed by utilizing the stresses and displacement at all interfaces, and by complying with the compatibility requirements at each interface. Computed results are compared with an available approximate solution and satisfactory agreement is established. The reported solution is exact and it is not limited to thin cylinders.