The interaction of shock waves with viscosity is one of the central problems in the supersonic regime of compressible fluid flow. The propagation of weak spherical shock waves in highly viscous uniform medium has been investigated by CCW method. It is found that the shock velocity and shock strength both decreases as shock advances for low viscous region of a medium to the high viscous region. The pressure and particle velocity behind strong shock decreases with adiabatic index and Small decreasement in the pressure and particle velocity is found with the increase in viscosity coefficient. It is shown that applications of the CCW method and the neglect of overtaking disturbances are equivalent.