External gear pumps are the most widely employed source of power in hydraulic applications, allowing good performance and low manufacturing cost. Generally, pumps with involute external gears are most commonly used. The undesired large pressure overshoots or spikes could be excited by virtue of the sudden volumetric change of meshing pockets. In practice, the spikes cause the gear machines to be noisy, inefficient, and have fatigue problems. In order to improve above issues, relief grooves are adopted practically. In this paper, the meshing pressure and the effects of relief groove configurations are considered through CFD analysis.