A new slicing algorithm that uses multiple sets of cutting planes to automatically determine parting curves for three-dimensional parts is proposed. In this algorithm, one set of cutting planes is used to generate the slicing profiles, and two others are used to determine the intersection points with the inner and outer loops of the parting curves. The algorithm provides a highly effective solution for handling complicated models that contain free-form surfaces. The features of the algorithm are highlighted in three case studies using tessellated geometry in STL file format as the input. The resultant parting curves overcome many problems inherent in the current methods and can be used by various downstream computer-aided design systems for three-dimensional mold design.