General properties of directed ordering near line defects in elastic crystals undergoing phase transition are studied using the two-component time-dependent Ginzburg-Landau equation. Upon quenching the system below its transition point, the temporal evolution of the order parameter in the vicinity of the defect is evaluated. The development of vortices is explored and their interaction with the structural defect is examined. Finally, phase transitions in improper ferroelectrics in the context of the model are discussed.