Abstract By modifying Rusanov's difference scheme as developed for a quasilinear hyperbolic system of partial differential equations in quasi-conservative form, a converging cylindrical shock problem in vibrationally relaxing gas has been studied in this paper. By comparing our results with available results in literature for inert gases, the effect of vibrational relaxation on such shock waves has been obtained. It has been shown that cylindrical shock waves in a vibrationally relaxing gas decreases in strength as it is propagating towards the axis. It has been observed that the effect of vibrational relaxation is to increase the growth rate of shock strength when it is propagating towards the axis. Further, it has been shown that the vibrationally relaxing character of the gas is to accelerate the shock convergence with the axis and thus decrease the convergence time.