This paper proposes a CSG-based representation scheme for heterogeneous objects including multi-material objects and Functionally Graded Materials (FGMs). In particular, this scheme focuses on the construction of complicated heterogeneous objects guaranteeing desired material continuities at all the interfaces. In order to create various types of heterogeneous primitives, we first describe methods for specifying material composition functions such as geometry-independent, geometry-dependent functions. Constructive Material Composition (CMC) and corresponding heterogeneous Boolean Operators (e.g. material union, difference, intersection. and partition) are then proposed to illustrate how material continuities are dealt with. Finally, we describe the model hierarchy and data structure for computer representation. Even though the proposed scheme alone is sufficient for modeling all sorts of heterogeneous objects, the proposed scheme adopts a hybrid representation between CSG and decomposition. That is because hybrid representation can avoid the unnecessary growth of binary trees.