The method of stationary phase and Lighthill's construction are used t
o develop the generalized Mach cones associated with MHD disturbances
generated by a source moving uniformly through a magnetized plasma. In
the frame of the source, the wave-number surface is obtained by Doppl
er shifting its counterpart in the plasma frame. This enables us to di
rectly apply stationary phase methods to deduce the stationary MHD str
uctures generated in the source frame. In the case of sub-fast flow ac
ross the magnetic field, these consist of two Alfven lines and two clo
sed hollow wings associated with the slow mode whose group velocity su
rface reflects the complicated cross-sectional shape of these hollow w
ings. In super-fast flow these Alfven and slow-mode disturbances lie i
nside the fast-mode Mach cone. Particular attention is given to the fi
ne structure of the slow mode. The results are relevant to the MHD dis
turbances created by the motion of a conducting body through a magneti
zed plasma, such as occurs in tethered satellite systems and the lo Ju
piter interaction.