The hydromagnetic stability of non-streaming bounded annular cylindrical interface having a tar mantle has been studied. The stability criterion has been derived, formulated in a dimensionless form and discussed. Some reported results have been obtained from the present general stability criterion as limiting cases. The longitudinal magnetic fields interior and exterior the fluid cylinder are stabilizing while the exterior transverse magnetic field is destabilizing. The different factors of the problem play an important role in stabilizing the model. As the Alfven wave velocity effect due to the magnetic field is much greater than that of the fluid speed, the destabilizing effect of the transverse field will be suppressed and stability sets in.