Ocean surface wave radiation stress represents the flux of momentum due to the waves. When waves are dissipated or reflected by sea ice, that momentum is absorbed or reflected, resulting in a horizontal forcing which frequently compresses the ice. In this work, wave radiation stress is used to estimate the compressive force applied by waves to the marginal ice zone (MIZ). It is balanced by an ice internal compressive stress based on Mohr-Coulomb granular materials theory. The ice internal stress can be related to ice thickness, allowing this force balance to be used as a model for the estimation of MIZ ice thickness. The model was validated and tested using data collected during two field campaigns in the St. Lawrence Estuary in 2016 and 2017. Modelled ice thickness was found to be consistent with the mean measured ice thickness over the conditions available. The range of validity of the model is discussed, and a definition of MIZ extent, based on the relative strength of wind and wave forcing, is proposed.