Our previous work on the simulation of packing processes was extended to study the liquid trickle flow down randomly packed beds. An algorithmic procedure with detailed geometrical description of packing elements was developed for tracking the liquid flow and holdup distributions in packed beds. Unlike the conventional continuum-based models such as the diffusion model, it goes into the subparticle scale to capture the geometrical characteristics of the packed bed. Three mechanisms of the trickle flow - film flow, dripping flow, and splash - were observed in packed beds, and the first two were captured in the model. At each point within a packed bed, liquid flow is simplified to two possible directions: vertically down and horizontally in the direction of the negative gradient of the packing surface. The 3-D geometric model constructed with the packing process simulation was used to determine the direction of the horizontal flow and fraction of the flow rate in each direction. By assuming that the liquid flow is uniform free surface flow, the Manning formula was used to predict the liquid holdup with the width of the liquid rivulet on a packing surface calculated by the Shi and Mersmann correlation. Metal Pall rings and metal Raschig rings were simulated with water as the fluid. Results of liquid flow distributions and average liquid holdup were validated against experimental data and semiempirical correlation from Billet et al.