The field of motion of sea ice is such that a Lagrangian element will be progressively deformed. The deformation can be resolved into a smooth part analogous to the distortion of a highly viscous fluid plus a random and discontinuous part having some similarity to the random motion of a turbulent fluid and the discontinuous motions of plate tectonics. The Lagrangian element spreads out at a rate determined by the mean field and by the random field, but the mean field usually is more important. The importance of the random field is that it gradually mixes the Lagrangian element with the surrounding ice. A mechanism for this mixing is discussed. The simplest mode of deformation for sea ice may be a finite shear displacement along a single crack. If the ice deforms in this way, first along one crack, then along another, and eventually along a sequence of randomly oriented cracks, the result will be a complete reshuffling of the ice pack. Nearby points disperse. Compact regions become fragmented. This model can be tested against observations of ice motion. In terms of the relative diffusion of pairs of points, the model predictions have a weak resemblance to actual ice behavior.