Contrary to high frequency (MHz-GHz) elastic data, at low frequencies (0.1-50 Hz) huge elastic softening (superelasticity) is usually found in the low symmetry improper ferroelastic phases (i.e., tetragonal or rhombohedral) of perovskite structured materials including SrTiO3, KMn1-xCaxF3, and LaAlO3. This giant elastic softening is caused by domain wall motion and can be suppressed with uniaxial stress. Taking into account the long range interaction of needle shaped domains and the repulsion between domain walls of finite thickness a free energy is constructed. The temperature variation of the elastic susceptibility is calculated which yields perfect fitting of the data. Within this soliton model we can also describe the measured effect of applied stress.