One of the functions of everyday human language is to communicate meaning. Thus, when one hears or reads the sentence, “John gave a book to Mary,” some aspect of an event concerning the transfer of possession of a book from John to Mary is (hopefully) transmitted. One theoretical approach to language referred to as construction grammar emphasizes this link between sentence structure and meaning in the form of grammatical constructions. The objective of the current research is to (1) outline a functional description of grammatical construction processing based on principles of psycholinguistics, (2) develop a model of how these functions can be implemented in human neurophysiology, and then (3) demonstrate the feasibility of the resulting model in processing languages of typologically diverse natures, that is, English, French, and Japanese. In this context, particular interest will be directed toward the processing of novel compositional structure of relative phrases. The simulation results are discussed in the context of recent neurophysiological studies of language processing.