In this paper, we study the effects of strong stretching in the horizontal plane of large-scale mesoscale ocean eddies using the theory of ellipsoidal eddies in the World Ocean. The objective is to theoretically determine the physical conditions for unbounded stretching eddies and also check the feasibility of these conditions in the ocean. We estimate the share of mesoscale ocean eddies that are elongated into filaments and then they redistribute energy from the mesoscale to the submesoscale.