The present study aims at the methodological improvement of the electrofreezing of supercooled water by applying oscillatory shear along with a homogeneous electric field in non-equilibrium molecular dynamics simulations of simple water models (such as TIP4P and SPC/E). The application of a planar Couette flow field accounts for a moderate speedup in the phase transition. Since the system goes through a nonergodic glassy state in the course of the process, it is not surprising that a macroscopic manifestation of the Lyapunov instability inherent in the equations of motion is observed. The formation of a conjectured high-density ice polymorph (ice XII) has been studied in terms of the applied electric and oscillatory flow fields. The threshold value of the electric field for the crystallization has been determined. The method of applying the oscillatory flow field was also investigated in detail. (C) 1998 Elsevier Science B.V. All rights reserved.