The relatively new technique of fluidized bed assisted abrasive jet machining (FB-AJM) is applied to finishing the inner surfaces of tubular Inconel 718 components. The effects of abrasive size, jet pressure, and machining cycle were evaluated, and the behavior of abrasive cutting edges acting against the surface during the process to remove material is accounted for. The finished surface was found to be highly dependent on jet pressure because it affects the abrasive contact against the surface as well as the finishing force acting on the abrasive, on the abrasive grain size, which controls the depth of cut, and on machining cycle, which controls the interaction time between the abrasives and the surface being finished. By altering these conditions, this process achieves surface roughness as fine as and imparts minimal additional residual stress on the surface. This study also reveals the mechanisms that determine the smoothing of the inner surface of Inconel 718 tubes and improve the form accuracy, i.e., the internal roundness of the Inconel 718 tube.