In this paper we describe a waves-in-ice model (WIM), which calculates ice breakage and the wave radiation stress (WRS). This WIM is then coupled to the new sea-ice model neXtSIM, which is based on the elasto-brittle (EB) rheology. We highlight some numerical issues involved in the coupling and investigate the impact of the WRS, and of modifying the EB rheology to lower the stiffness of the ice in the area where the ice has broken up (the marginal ice zone or MIZ). In experiments in the absence of wind, we find that wind waves can produce noticeable movement of the ice edge in loose ice (concentration around 70 %)-up to 36 km, depending on the material parameters of the ice that are used and the dynamical model used for the broken ice. The ice edge position is unaffected by the WRS if the initial concentration is higher (0.9). Swell waves (monochromatic waves with low frequency) do not affect the ice edge location (even for loose ice), as they are attenuated much less than the higher-frequency components of a wind wave spectrum, and so consequently produce a much lower WRS (by about an order of magnitude at least). In the presence of wind, we find that the wind stress dominates the WRS, which, while large near the ice edge, decays exponentially away from it. This is in contrast to the wind stress, which is applied over a much larger ice area. In this case (when wind is present) the dynamical model for the MIZ has more impact than the WRS, although that effect too is relatively modest. When the stiffness in the MIZ is lowered due to ice breakage, we find that on-ice winds produce more compression in the MIZ than in the pack, while office winds can cause the MIZ to be separated from the pack ice.