In this study, a theoretical study is carried out on the collision of two disk-like particles to understand the coagulation of disk-like particles suspended in liquid under a shear flow. The diameter of the particle is fixed at 2 μm while the length is varied so that the aspect ratio (length/diameter) varies from 0.1 to 0.4. The liquid viscosity is changed from 0.01 to 1 Pa s. The minimum Peclet number is 10, and the Brownian motion is considered to be negligible. Both hydrodynamic and van der Waals interactions are included in tracking the position and the orientation of each particle. The Hamaker constant is fixed at 1.06 × 10-20 J. The boundary integral formulation is used to calculate the hydrodynamic interaction. To obtain the kinetic constant of coagulation, the time-independent orientation distribution function for a particle is obtained under the noninteracting condition. The kinetic constant of coagulation is obtained by considering the presence of collision between two particles initially separated by a long distance, the orientations of two particles, and the flux of the liquid flow. The result shows that the kinetic constant of coagulation is reduced to approximately 1/3 of the value for the noninteracting particles when the viscosity is 1 Pa·s. As collision modes, side-side, face-edge, side-edge, and edge-edge are considered. The edge-edge mode is frequently observed in the given range of the aspect ratio. The collision mode does not change much from the noninteracting case except for the side-side mode.