The propagation of macroscopic phase boundary in material with CdS-type phase transition constitutive relation is investigated. The phase boundary is consisted of two segments corresponding to the new phase and mixed phase, respectively. The step by step approximation method can be applied to the new phase segment, however, the mixed phase segment can only be solved by numerical method. A sample problem is calculated of which the results of the step by step approximation method and numerical method fit to each other quite well. ©2000 American Institute of Physics.