Abstract: The Ginzburg-Landau (GL) equation is used to describe a wide class of first order phase transformations (PTs), which includes ferroelastic, martensitic, reconstructive, ferroelectric and magnetoelastic PTs, PTs in liquid crystals, twinning and dislocation generation. A new thermodynamic potential for stress-induced martensitic PTs was recently developed (V. I. Levitas, D. L. Preston and D. W. Lee, Phys. Rev. B, 134201, 2003). Method that introduces an athermal resistance to interface propagation for GL approach for PTs is developed. It consists of introducing an oscillating field of stresses (due to various defect or Peierls barrier) or jump in chemical energy. It removes essential drawbacks in GL modeling: it arrests experimentally observed microstructures that otherwise converge to a single phase and reproduces rate-independent stress PT hysteresis (V. I. Levitas and D. W. Lee, Phys. Rev. Lett., 245701, 2007). A similar approach can be applied for twinning, dislocations and other PTs.