We introduce a new class of elliptically modulated self-trapped singular beams in isotropic nonlinear media where nonlocality plays a crucial role in their existence. The analytical expressions in the highly nonlocal nonlinear limit of these elliptically shaped self-trapped beams, or ellipticons, is obtained and their existence in more general nonlocal nonlinear media is demonstrated. We show that the ellipticons represent a generalization of several known self-trapped beams, for example vortex solitons, azimuthons, and the Hermite and Laguerre solitons clusters. For the limit of the highly nonlocal nonlinear medium, the ellipticons are described in close form in terms of the InceGauss functions.