Inclusion of effects of disturbances behind the shock waves moving in uniform and non-uniform medium modifies the approximate method used to investigate their propagation. Using modified CCW Method an attempt has been made to study the propagation of strong cylindrical shock waves including the effect of disturbances behind the shock through an ideal and rotating gas at permissible shock front locations for an arbitary initial density distribution of the form, say, p₀= p1 og(1+lr), where is the density at the axis of symmetry and l is non-dimensionalyzing constant.The numerical estimate of the flow variables have been computed at only on those values of propagation distance r which are permitted by the entropy distribution condition. The result obtained has been presented through graph and compared with the earlier work.