The Rankine-Hugoniot relations of an axial shock in cylindrical non-neutral plasma with current, electric and magnetic field are presented. These relations are all dependent on the radius of cylindrical plasma, and markedly different from the one-dimensional (i.e., nonradially dependent) case. These two-dimensional Rankine-Hugoniot relations cause at least two important new results. First, the radial profiles of the shock downstream parameters are always different from the upstream profiles due to the magnetic effects. Second, the critical Mach number for the shock existence will depend on the shock carried current (i.e., magnetic field). As an example, a set of shock downstream profiles is provided numerically when the upstream profiles are taken as a kind of typical equilibrium profiles of a Z-pinch-Bennett profiles. By comparing the downstream profiles to the corresponding upstream profiles, the dependents of both the amplitudes and profiles of the downstream parameters on the shock carried current are shown.