A collisional rheology for an idealized two-dimensional flow of a fragmented ice field is derived. This fragmented ice field is modeled as an assembly of identical smooth disks. Collisions between neighboring disks are caused by the mean deformation field. These collisions transfer momentum which produces the internal stresses in the deforming ice field. By equating the collisional energy losses to the deformational energy, a relationship between the stress and strain rate is quantified. To demonstrate the essential idea, an analytical derivation is first given under quite restricted assumptions. A Monte Carlo simulation is then developed to provide a more general approach for the analysis. It is found that the collisional stresses are proportional to the square of disk diameter and the square of the deformation rate. The magnitude of stresses is also found to increase rapidly as the collisional restitution of disks increases. The collisional rheology yields zero tensile strength. The associated normal flow rule commonly used in the plastic rheology is not valid in the collisional rheology. It is found that the collisional stresses are very small. Consequently, the resulting stress divergence is estimated to be much lower than the air stress typically encountered in the marginal ice zone. However, these collisional stresses become singular as the maximum compactness is reached, indicating that a different mechanism may exist in that extreme. ¿ American Geophysical Union 1987