In this study I am going to propose a semantic analysis of the English reduced relatives within the framework of the Conceptual Structwes Theory. The study of conceptual structures has continued for more than a decade and has become one of the most popular systems for Natural Language Processing. As a new knowledge representation model, conceptual graphs have a strong basis in cognitive psychology. Sowa, who developed this theory, gives compelling evidence that something like conceptual graphs are built and remembered during cognitive processing in the mind. By using a computer representation for models resembling that of the mind, the chance of information loss is minimized in the translation between user and computer. With this merit, conceptual graphs can be best way to account for the various, sometimes peculiar linguistic phenomena.