Solar modulation gives rise to intensity depletion and directional anisotropies in the distribution of galactic cosmic rays (GCRs). These anisotropies are observed to extend into the 100 GV range, where the gyro-radius of GCRs becomes large and the robust diffusive equation of Parker is no longer applicable. We consider both diffusive and non-diffusive models to describe the high-rigidity regime of solar modulation. Our non-diffusive approach employs a model based on calculating energy losses suffered by GCRs along their trajectories through the heliosphere. We track GCR trajectories backward in time. A random magnetic field component is also added to account for scattering. The role of the wavy heliospheric current sheet (HCS) is studied in the two different polarity states of a 22-year magnetic cycle changing the tilt angle of HCS. Simulation results are compared with 44 years of observational data from the Muon Detector in Nagoya (Japan) and Neutron Monitors. We present preliminary simulation data to demonstrate robust qualitative trends. Some implications of the simulation results are discussed.