Inverse offsetting is a special type of Minkowski sum operation with a solid model and an inversed shape of a milling cutter. In the NC machining, geometric simulations of the milling operation are often performed prior to the actual machining to visualize the result shape of the workpiece. Inverse offsetting of this workpiece shape is useful for automating some process planning tasks, especially a task for determining milling regions for the following machining operations. Most milling simulation programs use discrete Z-map models for representing the workpiece shape. In this paper, an algorithm for inverse offsetting the Z-map model is proposed. Our algorithm computes dense zig-zag curves covering the Z-map model, then it generates the swept volume of the inversed cutter moving along the curves to obtain the inverse offset shape of the model. The proposed algorithm is implemented and an experimental process planning assistance program using this technology is demonstrated