The aim of this research is the investigation of the evolutionary progression that the vaulted and arched structures followed. The choice of this theme relied upon our effort to study the genesis of such structures that differ from the popular structural system of Ancient Greeks, beam upon columns, and to check their constructional methods through centuries. Our field of research constituted of stone constructions were arches or vaults were used in order to span gaps and they are detected at Greece or at the west side of Asia Minor, between 17^th and 1^st century BC. We consider that delving into these special structures will make it easier to understand the reason of their limited use despite the fact that they were known and evolved at those times. Moreover we will make an attempt to answer the question that derives from the sudden transition from the corbelled principle of building to the principle of the true arch, during the 4^th century BC