The blast wave solutions for the axisymmetric flow fields associated with a family of power law shocks, y sub s equals approximately x to the n power, were modified to properly account for the entropy layer near the surface of the body. The method of inner and outer expansions was used. It was shown that this method is of limited usefulness for n only slightly greater than 1/2 due to the slow convergence of the inner expansions, but for (gamma 2)/(3 gamma 2) less than or equal to n <1 the expansions converge rapidly enough for the method to be useful. The case n 1/2 is singular and causes no difficulty. In the range (gamma 1) /(2 gamma 1) less than or equal to n<1 the body shape given by blast wave theory is correct, but the blast wave flow profiles must be modified near the body.