  A theoretical investigation has been made on the propagation of ion-acoustic
(IA) shock waves (IASHWs) in a magnetized pair-ion plasma having inertial warm
positive and negative ions, and inertialess super-thermal electrons and
positrons. The well known Burgers' equation has been derived by employing the
reductive perturbation method. The plasma model supports both positive and
negative shock structures under consideration of super-thermal electrons and
positrons. It is found that the oblique angle ($\delta$) enhances the magnitude
of the amplitude of both positive and negative shock profiles. It is also
observed that the steepness of the shock profiles decreases with the kinematic
viscosity of the ion, and the height of the shock profile increases (decreases)
with the mass of the positive (negative) ion. The implications of the results
have been briefly discussed for space and laboratory plasmas.
