Most of Ellison's research has centered on developing theoretical models of particle acceleration mechanisms in astrophysics. He was among the first to recognize the importance of nonlinear effects in diffusive shock acceleration and he developed Monte Carlo computer simulations to investigate this effect. This work has been applied to the production of cosmic raysin supernova remnants as well as to collisionless shocks in the heliosphere. He was also among the first to investigate the effects of efficient particle acceleration in relativistic shocks with applications to gamma-ray bursts. Other research accomplishments associated with shocks include the modeling of the production of strong magnetic turbulence in shocks and the use of particle-in-cell computer simulations to investigate the injection of thermal particles into the diffusive shock acceleration mechanism.