In this paper, a developed three-dimensional model combining finite-element and smoothed-particle hydrodynamics approaches is presented. It incorporates a crystal-plasticity theory for vibration-assisted machining into ABAQUS/Explicit software by using a user-defined subroutine VUMAT. The paper presents quantitative comparison of cutting-force variation for VAM and conventional machining with identical cutting parameters for anisotropic workpieces. The obtained simulation results demonstrated that the (101) crystal orientation with a cutting direction at 30° had the highest reduction in a cutting force for three levels of vibration amplitude (10, 20 and 30 μm) and three levels of frequency (15, 20 and 25 kHz).