In this study a theoretical study is carried out on the binary collision of round-sided disks (RSD) suspended in a Newtonian fluid under a simple shear flow. RSD is composed of a disk part and a half-torus part which circumscribes the side of the disk. The diameter of the disk is fixed at 2 μm while the thickness and the half-torus size are varied so that the aspect ratio varies from 0.13 to 0.288. The liquid viscosity is changed from 0.01 to 1 Paㆍs. The hydrodynamic force and van der Waals force with the Hamaker constant of 1.06 x 10-20 J are considered in tracking the position and the orientation of each particle. The Brownian motion is considered to be negligible. The collision of two particles initially separated by sufficiently a long distance is considered and the kinetic constant of coagulation is obtained by considering the presence of collision, the orientations of two particles and the flux of liquid flow. The result shows that the kinetic constant of coagulation is reduced to approximately 1/4 of the kinetic constant of non-interacting particles by the hydrodynamic interaction when the viscosity is 1 Pa·s. As collision modes, side-side and side-edge are considered. Side-side mode is found to be the dominant mode of collision for differing aspect ratio and differing viscosity of the liquid. The dominance of the side-side collision mode implies the formation of two-dimensional flocs in the shear flow.