We present detailed results for the structural and rheological properties of unknotted and unconcatenated ring polyethylene ( PE) melts under shear and elongation flows via direct atomistic nonequilibrium molecular dynamics simulations. Short ( C78H156) and long ( C400H800) ring PE melts were subjected to planar Couette flow ( PCF) and planar elongational flow ( PEF) across a wide range of strain rates from linear to highly nonlinear flow regimes. The results are analyzed in detail through a direct comparison with those of the corresponding linear polymers. We found that, in comparison to their linear analogs, ring melts possess rather compact chain structures at or near the equilibrium state and exhibit a considerably lesser degree of structural deformation with respect to the applied flow strength under both PCF and PEF. The large structural resistance of ring polymers against an external flow field is attributed to the intrinsic closed-loop configuration of the ring and the topological constraint of nonconcatenation between ring chains in the melt. As a result, there appears to be a substantial discrepancy between ring and linear systems in terms of their structural and rheological properties such as chain orientation, the distribution of chain dimensions, viscosity, flow birefringence, hydrostatic pressure, the pair correlation function, and potential interaction energies. The findings and conclusions drawn in this work would be a useful guide in future exploration of the characteristic dynamical and relaxation mechanisms of ring polymers in bulk or confined systems under flowing conditions. (C) 2016 The Society of Rheology.