This document numerically simulates instabilities in counter flows of viscoelastic fluids using two rheological models, Oldroyd-B and De Witt. Two instability mechanisms are observed: with low Reynolds numbers (Re < 0.1), circular vortex structures arise near the central point; with moderate Reynolds numbers (Re > 3), the instability onset resembles classical inertial instabilities. Very similar results are obtained for both fluid models, unlike in other flow problems. The instabilities are attributed to elastic energy accumulating and dominating over viscous forces at high Weissenberg numbers.