Undulation is a biological form of propulsion involving oscillatory motions of surfaces typically for propulsion. In this effort, computational fluid dynamics (CFD) is used to advance the understanding of pairs of undulating foils for moderate Reynolds number flows, how they interact, and their factors leading to efficiency. The CFD accuracy is established through a benchmark study using experimental data of heaving hydrofoils. Following this, a pair of foils are prescribed heave-pitch motions and evaluated in a parametric study of various displacements to understand the effects of shed vortexes on heaving and pitching foil boundaries. Lastly, a parametric study is performed for the pair of undulating foils as well as in the context of schooling, undulating objects. Our results show multiple fluid responses to varying motion parameters and the effects of vortex shearing on thrust generation.