Numerical simulations of the motion of red blood cells (RBCs) freely suspended in shear flow have been successfully performed to investigate the nature of pairwise interception of RBCs using a fluid-particle interaction method based on the arbitrary Lagrangian-Eulerian (ALE) method and a dynamic mesh method. The applicability of the interaction method that we used was validated by comparing the simulation results with an analytical solution for an elliptical particle in shear flow. We found that positive and negative transverse shifts of the RBCs take place during the interceptions, yielding a non-zero RBC self-diffusivity, and that a phase shift occurs during the rotating behavior and lasts even after the separation. The behaviors of the approaching RBCs are adjusted by interactions with the surrounding flow fields during interception. The pressure between a pair of RBCs causes either an attractive or repulsive force. The nature of the pairwise interception is influenced not only by the flow fields but also by kinematic characteristics (i.e., instantaneous translational and rotational behavior) of the two RBCs.