The modelling of a vibration-assisted (VA) machining using the Particle Finite Element Method (PFEM) is developed in this work. Vibration-assisted machining presents some advantages compared with the conventional technique as it increases the life of cutting tools, reducing the surface wear and producing manufactured parts with better surface integrity. These improvements are achieved because the cut is carried out developing lower cutting forces and lower temperatures, facilitating chip separation and reducing friction forces. Those virtues stem from the volume and surface effects caused by vibration emerging as softening response of the material. In this regard, the numerical solution of VA machining process should consider the softening effects in the constitutive modelling of the workpiece. In addition, a robust remeshing technique is required in finite element simulation of machining process due to inherent large strains and deformations. The Particle Finite Element Method (PFEM) is a well-established tool in numerical solutions which uses particles to characterize the continuum based on lagrangian description of the domain. In complex large deformation phenomena like machining, the application of PFEM showed excellent results [1,2]. Here, the PFEM is employed to model the VA machining considering the acoustic-plasticity softening effects of the material comparing different techniques: using additive, multiplicative and coupled terms. The contact domain theory is used in the interaction of tool and workpiece considering both frictionless and frictional contact effects in cutting forces and temperatures. The ultrasonic vibration and its effects on the machining parameters are analyzed by modelling a set of turning examples with transient vibration.