The Marginal Ice Zone (MIZ) is a highly dynamic region between the open ocean and the inner ice pack. The ice over this region is subjected to waves, introducing new forces but also changing the ice from a cohesive material to a mobile collection of floes. Until recently, the challenges posed by in-situ ice measurements in the MIZ prevented a detailed characterization of changes in the ice cover. The rapidly changing conditions over short distances have also prevented detailed numerical simulations. Recent developments in observational and computational capabilities allow further investigations of the physical processes for ice formation and wave-ice interactions in the MIZ. Many features of the MIZ remain to be explained and quantified, particularly rapid ice movement near the ice edge and ice thickening under wave pressure. In order to investigate these and support future field and numerical studies, a model of the MIZ is developed with a new numerical method better suited for high resolution. Simulations of waves causing ice compaction and the ice edge jet are then performed to detail the expected impacts of waves on sea ice. The potential of numerical improvements in sea ice models to obtain greater efficiency and accuracy at high resolutions is successfully demonstrated. The addition of the wave radiative stress allows the generation of realistic thickness profiles, provided that the sea ice strength is modified to represent the difference between pack ice and thinner ice. With the same modifications, obliquely incident waves on the ice edge produced an ice edge jet with a range of characteristics depending on wave parameters and modeled interactions. The magnitude of wave attenuation in sea ice and the ice strength are found to be very important factors in the simulations. Consideration of wave effects on ice thickness and drift speed are also shown to have potential to increase both open water and ice formation.