In two-dimensional (2D) free-form contour machining by using a straight (flat) end mill, conventional contour parallel paths offer varying cutting engagement with workpiece, which inevitably causes the variation in cutting loads on the tool, resulting in geometric inaccuracy of the machined workpiece surface. This paper presents an algorithm to generate a new offset tool path, such that the cutting engagement is regulated at a desired level over the finishing path. The key idea of the proposed algorithm is that the semi-finish path, the path prior to the finishing path, is modified such that the workpiece surface generated by the semi-finish path gives the desired engagement angle over the finishing path. The expectation with the proposed algorithm is that by regulating the cutting engagement angle along the tool path trajectory, the cutting force can be controlled at any desirable value, which will potentially reduce variation of tool deflection, thus improving geometric accuracy of machined workpiece. In this study, two case studies for 2D contiguous end milling operations with a straight end mill are shown to demonstrate the capability of the proposed algorithm for tool path modification to regulate the cutting engagement. Machining results obtained in both case studies reveal far reduced variation of cutting force, and thus, the improved geometric accuracy of the machined workpiece contour.