Gear hobbing, as any cutting process based on the rolling principle, is a signally multiparametric and complicated gear fabrication method. Although a variety of simulating methods has been proposed, each of them somehow reduces the actual three-dimensional (3D) process to planar models, primarily for simplification reasons. The paper describes an effective and factual simulation of gear hobbing, based on virtual kinematics of solid models representing the cutting tool and the work gear. The selected approach, in contrast to former modeling efforts, is primitively realistic, since the produced gear and chips geometry are normal results of successive penetrations and material removal of cutting teeth into a solid cutting piece. The algorithm has been developed and embedded in a commercial CAD environment, by exploiting its modeling and graphics capabilities. To generate the produced chip and gear volumes, the hobbing kinematics is directly applied in one 3D gear gap. The cutting surface of each generating position (successive cutting teeth) formulates a 3D spatial surface, which bounds its penetrating volume into the workpiece. This surface is produced combining the relative rotations and displacements of the two engaged parts (hob and work gear). Such 3D surface “paths” are used to split the subjected volume, creating concurrently the chip and the remaining work gear solid geometries. This algorithm is supported by a universal and modular code as well as by a user friendly graphical interface, for pre- and postprocessing user interactions. The resulting 3D data allow the effective utilization for further research such as prediction of the cutting forces course, tool stresses, and wear development as well as the optimization of the gear hobbing process.