Martensitic transformations are shown to be driven by the interplay between two fluctuating strain components. No soft mode is needed, but a central peak occurs representing the dynamics of strain clusters. A two-dimensional magnetic-analog model with the martensitic-transition symmetry is constructed and analyzed by computer simulation and by a theory which accounts for correlation effects. Dramatic precursor effects at the first-order transition are demonstrated. The model is also of relevance for surface reconstruction transitions.