ABSTRACTThe modular pebble-bed nuclear reactor (PBR) is a candidate Generation IV reactor being developed. The pebble flow in the very slow draining of fuel pebbles draws attention for its implications on core physical design and reactor physics analysis. One of the effective and simplified methods to address this problem is the kinematic model which is based on continuous theory to derive a diffusion equation for vertical velocity. This paper investigates the appropriate numerical solutions for the kinematic model of pebble flow velocity profiles in PBR geometry. Our method is based on a previously proposed transformed Cartesian coordinates and uses the implicit Crank–Nicholson integration scheme with two different treatments of the boundary conditions. Validations show that this numerical solution gives preferable agreements with the experimental results in the reference. Finally, the simulated velocity profiles are applied in the investigation of two pebble burnup-related issues, which are the pebble residence time prediction and the channel scheme in realistic high-temperature reactor pebble-bed modules reactor core geometry.