A Computational Fluid Dynamics based erosion model is presented to numerically study the influence of ultrasonic vibrating workpiece on the particle impact erosion of glasses involved in the abrasive slurry jet (ASJ) machining process. The Eulerian-Lagrangian method and dynamic meshing technique are used to represent the ASJ flow and the periodical movement of the workpiece, while the particle rebound model and semi-empirical erosion model for glasses by considering the brittle-ductile transition are employed to simulate the impact erosion process, respectively. It has been found from simulation that the combined effects of stagnation zone and brittle-ductile transition that results in W-shaped cross-sectional profiles in ASJ micro-machining of holes in experiment. However, in the stagnation zone with an ultrasonic vibrating workpiece a periodical variation of static pressure is observed and its influence on the particle trajectory near the stagnation has been analysed. It is found that the relative movement between the ASJ flow and workpiece rather than the relative location of the work piece far away from the nozzle exit results in the dynamic impacts of particles on the target surface which not only increase the average erosion rate but also contribute to the uniform distribution of the erosion area on the target surface. Further, the erosion induced by the viscous flow around the ASJ directly impact zone is found to be enhanced due to the more multiple impacts by the particles following the viscous flow that is affected by the ultrasonic vibrating workpiece, which would enlarge the ASJ machining area as the impact event progresses. These findings from the simulation are significant for the improvement of the ASJ micro-machining efficiency and quality. (C) 2016 Elsevier B.V. All rights reserved.