Vibration assisted nano impact-machining by loose abrasives (VANILA) is a novel nanomachining process that combines the principles of vibration-assisted abrasive machining, and tip-based nanomachining, to perform target specific nano abrasive machining of hard and brittle materials. An atomic force microscope (AFM) is used as a platform in this process wherein, nano abrasives, injected in slurry between the workpiece and the vibrating AFM probe, impact the workpiece and cause nanoscale material removal. The objective of this study is to develop a mathematical model to determine the material removal rate (MRR) in the VANILA process. The experimental machining results reveal that the material removal happens primarily in ductile mode due to repeated deformation which happens at near normal angles of impact. A predictive model for MRR during the VANILA process is analytically developed based on elastoplastic impact theory for normal angles of impact. The model is validated through a series of experiments performed on silicon and borosilicate glass substrates and the results confirm that the model is capable of predicting the machining results within 10% deviation.