It is provided a computer-implemented method for simulating the machining of a workpiece with a cutting tool having a cutting part and a non-cutting part. The method comprises providing (S10) a modeled volume representing the workpiece and a trajectory of the cutting tool; determining (S20) a colliding sweep of the cutting tool, wherein the colliding sweep represents the volume swept by the non-cutting front of the cutting tool when the cutting tool follows the trajectory; testing (S30) a collision with the workpiece according to the determining (S20) step.s Such a method improves the simulation of the machining of a workpiece with a cutting tool.