Based on the novel viewpoint that ring polymers, with their closed-loop molecular geometry, are naturally defined by an intrinsic two-dimensional topological surface, we analyzed the fundamental structural characteristics and dynamic mechanisms of ring polymers under shear flow. We then proposed several representative physical measures that could effectively be used to characterize the overall ring structure and dynamics. To directly quantify the physical properties, an efficient numerical algorithm was further developed to effectively describe various complex curved surfaces represented by flexible ring polymers. Both dilute and melt ring systems were analyzed under shear flow with a wide range of flow strengths using atomistic nonequilibrium molecular dynamics and coarse-grained Brownian dynamics simulations. The general properties of the interchain influence determined from the dilute and melt systems are informative for predicting the structural and dynamical characteristics of semidilute polymer solutions with respect to the polymer concentration. The present analysis can be extended to various ring-type polymers such as branched ring polymers, ring-shaped biological molecules, and twodimensional polymers.