In the dynamic theory of martensitic transformations, the wave mechanism of controlling martensite crystal growth is determined by the superposition of wave beams of quasi-longitudinal (or longitudinal) waves carrying the "tensile-compression" deformation in the orthogonal directions. The wave beam formation is considered to be a result of the formation of excited (vibrational) states. The existence of transformation twins is interpreted as a result of a matched propagation with respect to long-wave (l waves) and short-wave (s waves) shifts. The matching condition is analyzed for the gamma-alpha martensitic transformation in iron-base alloys. It is shown for the first time that the transition to a degenerate twin structure with the allowance for the medium discreteness enables one to estimate the dislocation density in crystals with habit {557}, which agrees with that observed experimentally
