Unlike the phases of ordinary fluids, solid phases are often found to occur in metastable equilibrium. At constant temperature, a stress-extension test on a bar made of a material which allows the co-existence of two phases will often produce a large hysterysis loop. It is then impossible, by static measurements alone, to determine the values of stress ** and temperature θ* at which the two phases have the same specific free energy. I show that by a measurement of the jump in temperature across a propagating phase boundary, (Τ*, θ*) can be determined in several cases of interest. The analysis offers insight into the general behavior of propagating phase boundaries as well as the thermodynamics of solid phases. The discussion is centered around the so-called shape-memory alloys.