This paper investigates the impact on free abrasive machining (FAM) process using a vibrating wire with an oscillating boundary condition. The experimental results show that the vibration of wire in slurry with abrasive grits can result in material removal due to FAM on brittle material. We present a theoretical model of a wire moving axially at a constant speed, subject to an oscillating boundary condition with damping, and derive an analytical solution of the partial differential equation of motion. Based on the modeling and analysis, the frequency of vibration of wire corresponds to the frequency at the oscillating boundary at steady state. The damping factor suppresses the lateral movement of wire from the fixed boundary to moving boundary when it is increased. The change of axial wire speed or the oscillating frequency at boundary can counteract the suppression on the vibration response induced by increased damping factor. This study also presents an experimental study using an experimental setup of a slurry-fed wire with a periodic excitation to study the FAM process on silicon. The results of experiments show that vibration of wire can impart the silicon carbide abrasive grits in slurry to generate observable grooves and fractures on the surface of silicon in just a few minutes. The grooves and fractures are generated by the indentation of abrasive grits via loading and unloading on the silicon surface. When the vibrating wire is only fed with water without abrasives or under a dry condition, compressive deformation with shallow grooves on silicon is observed; however, the surface is found to be free of surface features of indentation and scratching. Furthermore, evidence of both wire compression and abrasive machining is more pronounced at the edges of silicon specimen, especially at the edge close to the periodic excitation, which is consistent to our modeling.