We study diffusionless transformations in solids which involve a sudden change of shape at a certain temperature. We assume the existence of a free energy which depends on the local change of shape and the temperature. Properties of this function reflect the underlying symmetry of the parent and product phases and an exchange of stability from parent to product phase as the body is cooled through the transformation temperature θ0. We concentrate on two questions: (i) How can loads be applied to cause the body to transform to a particular variant of the product phase at or above θ0? (ii) Can the parent phase be recovered by applying some system of loads at or below θ0? Theory and experiment are compared for thermoelastic martensitic transformations in shape-memory materials and for the α-β transformation in quartz.