Sculptured surfaces are widely used in commercial products and industrial designs because of their aesthetically pleasing shape characteristics. In such instances, it often becomes necessary to model the part using compound surfaces that consist of several individual sculptured surface patches. In comparison to single surface patches, compound surfaces give rise to additional challenges in making process planning decisions. In this paper, several fundamental issues relevant to patch-by-patch finish machining of compound sculptured surfaces are examined. In particular, efficient procedures for determination of the maximum gouge-free tool size, detection and avoidance of gouging, identification of the best isoparametric cutter path, and determination of an efficient machining sequence of the composing patches are presented.