The propagation of a cylindrical shock wave in a rotational axisymmetric non-ideal dusty gas in the presence of conductive and radiative heat fluxes with increasing energy, which has variable azimuthal and axial fluid velocities, is investigated. The dusty gas is assumed to be a mixture of non-ideal (or perfect) gas and small solid particles, in which solid particles are continuously distributed. Similarity solutions are obtained and the effects of the variation of the heat transfer parameters, the parameter of non-idealness of the gas, the mass concentration of solid particles in the mixture and the ratio of the density of solid particles to the initial density of the gas are investigated. It is shown that the heat transfer parameters and the parameter of non-idealness of the gas, both, decrease the compressibility of the gas and hence there is a decrease in the shock strength.