A parametric shape grammar of the traditional Malay houses (TMH) built in the past century is presented. The grammar, which consists of rules for generating the form and structure of TMH, is derived from simple geometric representations of the houses. The rules first derive the basic unit structures that form the shapes of the TMH. Nine basic shapes have been identified that form the main vocabulary elements of the grammar. Parameterized polygons and lines define each basic shape. Ranges of values assigned to the variables describing the parameterized polygons and lines are presented. The shape addition rules are used to characterize the compositional aspects of TMH style. Evidences of these basic shapes or their combinations have been documented by previous researchers and are used as a way of explaining the built forms of the TMH. The scope of the study is currently limited to the original TMH of the bumbung panjang (long roof) type in which the key features of the houses are easily discernible from the side view.