Ultrasonic degradation of polymers is distinguished from thermal degradation by: midpoint rather than random chain scission; a lower limit of molecular weight (MW), xf, below which the polymer will not undergo midpoint scission; and possible biomodal distribution evolving with time. The molecular-weight distribution (MWD) is governed by a population-balance equation whose time dependence is deduced from MW moments. To examine if ultrasonically induced reactions have similarity solutions, the moment equations were considered in terms of the time evolution of generalized gamma distribution parameters. The rate coefficient for chain scission is assumed to depend on MW, x, as K (x - xf), where xf is the limiting MW. The MWD approaches a similarity solution (with a polydispersity of 1.5) only when limiting MWxf is zero. This study also provides an exact analytical solution for the MWD, showing how the MWD can evolve, with reaction time, from an unimodal distribution to a bimodal distribution. Numerical solutions are presented for cases when a polymer undergoes a reversible chain-end scission along with midpoint chain scission. The rate coefficients for chain-end scission and polymerization are assumed independent of MW. The theory satisfactorily explains experimental observations.