Many displacive solid-solid transformations, despite being first order, show pronounced precursor effects, such as the mesoscopic, micron-scale, ‘‘tweed’’ pattern seen in shape-memory alloys. We model this tweed theoretically using a nonlinear, nonlocal elastic free energy, and argue that quenched concentration inhomogeneities drive the local tweed modulations. We report (1) the construction of a model for {11}/〈11¯〉 shear transformations in square systems, (2) a simulation including concentration inhomogeneities, and (3) a mapping of the disordered 2D martensite onto an infinite-range spin model, identifying tweed with the spin-glass phase.