Abstract The accurate evaluation of the instantaneous undeformed chip thickness (IUCT) plays a crucial role in the modeling of milling processes. However, the vibrations of the tool-workpiece system can make conventional IUCT models either inaccurate or not applicable. This paper introduced the concept of surface function to describe the milled surface, through which the IUCT can be readily computed. The evolution of this surface function is governed by a partial differential equation (PDE) in the form of a balance law, and the material removal process is characterized by discontinuous conditions at the cutters. A finite volume algorithm is adopted to solve the proposed PDE with discontinuous conditions at the cutters. Through a case study of the asymmetric cutting process, the surface function method demonstrates two main advantages over typical conventional methods: (i) a detailed description of IUCT evolution considering the influence of the initial shape of the workpiece and (ii) a general framework to accurately compute the IUCT. This method shows a promising potential for computing the IUCT when simulating in numerical simulations.