The jump conditions across a shock front in a thin magnetic flux tube are studied by purely analytical means. Some properties of magnetohydrodynamic shock waves in extended media are shown also to hold in the more complicated case of thin magnetic flux tubes. It is shown that flux tube shock waves are always compressive, thus being accompanied by a weakening of the magnetic field strength and increase of the tube radius. Some consequences of this are examined, such as the sub- or supercritical character of the flow velocity with respect to the Alfvén, sound and "tube" speeds. The range of variation of the ratios of the different variables across the shock front is determined along with the equivalent of the Hugoniot curve and further properties of the shocks in magnetic flux tubes. The analogies and differences with HD and MHD shocks in extended media are pointed out. Finally, some implications of the shock wave structure for the solar atmosphere are briefly discussed.