It is known that interplanetary traveling shock waves can strongly disturb the Earth's magnetosphere (e.g., Blake et al., 1992; Reeves, 1996). In recent years, published hydromagnetic simulations have illustrated how such shock waves cause large distortions in the geomagnetic field, substantial transient induction electric fields and a compression of the magnetospheric topology (e.g., Li et al., 1993, 1996; Hudson et al., 1996, 1997). Particle observations in the magnetosphere following the March 1991 event show that pre-existing particle fluxes can be strongly and suddenly accelerated on a time scale of a small fraction of a trapped particle drift time scale around the Earth. Such short time scales appear incompatible with bodily injection phenomena from the exterior of the magnetosphere. Modeling has been carried out starting with the suddenly accelerated in-situ particle fluxes and following the subsequent relaxation process.