This report recapitulates the known results for similarity solutions for the flow problem of a strong converging shock in spherical or cylindrical symmetry and extends that work in four ways: parameters of the standard solutions are given for a large number of values of ..gamma..; some new, non-analytic solutions are exhibited for relatively large values of ..gamma..; the standard solutions are examined more thoroughly in the limits ..gamma -->..infinity and ..gamma -->..1; and solutions, existing only in a narrow band of values of ..gamma.., are given for the problem of two converging shocks. 7 figures, 4 tables.