We study the combined effect of elastic anisotropy and disorder on the microstructure and thermodynamic behavior in alloys undergoing a martensitic transformation. Within a Ginzburg-Landau free-energy framework we find the region in the parameter space where a ferroelastic glassy state exists without twinning. We find that such a glassy state is of kinetic origin rather than due to geometrical frustration. The glassy behavior is characterized by simulating zero-field-cooling/field-cooling curves for different values of anisotropy and disorder. Finally, we discuss experimental implications for Fe-Pd and Ni-Ti alloy