ABSTRACT The interpretation of recent observations of bow shocks around O-stars and the creation of corresponding models require a detailed understanding of the associated (magneto-)hydrodynamic structures. We base our study on 3D numerical (magneto-)hydrodynamical models, which are analysed using the dynamically relevant parameters, in particular, the (magneto)sonic Mach numbers. The analytic Rankine–Hugoniot relation for HD and MHD are compared with those obtained by the numerical model. In that context, we also show that the only distance which can be approximately determined is that of the termination shock, if it is an HD shock. For MHD shocks, the stagnation point does not, in general, lie on the inflow line, which is the line parallel to the inflow vector and passing through the star. Thus an estimate via the Bernoulli equation as in the HD case is, in general, not possible. We also show that in O-star astrospheres, distinct regions exist in which the fast, slow, Alfvénic, and sonic Mach numbers become lower than one, implying subslow magnetosonic as well as subfast and subsonic flows. Nevertheless, the analytic MHD Rankine–Hugoniot relations can be used for further studies of turbulence and cosmic ray modulation.