The machining of sculptured surfaces like molds and dies in 3-axis milling relies on the chordal deviation, the scallop height parameter and the planning strategy. The choice of these parameters must ensure that manufacturing surfaces respect the geometrical specifications. The current strategies of machining primarily consist in driving the tool according to parallel planes which generates a tightening of the tool paths and over quality. The constant scallop height planning strategy has been developed to avoid this tightening. In this paper, we present a new method of constant scallop height tool path generation based on the concept of the machining surface. The concept of the machining surface is exposed and its use to generate constant scallop height tool paths. The approach is confronted with existing methods in terms of precision and in particular its aptitude to treat curvature discontinuities.