Various theories explaining the origin of coral reefs have been proposed since Darwin. However, the theoretical basis of the worldwide geographical distribution of coral reefs has not always been clear, as reviwed in Chapter 1. A new model regarding the geographical distribution of coral reefs is presented in this paper (Fig. 1). The model postulated is as follows. Assuming that the continental shelf with a smooth surface extends from 30°N to 30°S, and that fluctuations in sea level and sea surface temperature repeat with the same magnitude during the Quaternary period, the geographical distribution of coral reefs can be expected to exhibit the following features. 1. In seas permitting the formation of coral reefs even during glacial ages, coral reefs would tend to grow at the shelf edge with a subsequent rise of sea level. The thickness of the coral reef limestones would be equivalent to the amount of the sea level changes. The reef type in such sea areas would be a barrier reef with pinnacles and knolls in a deep lagoon. 2. The width of a coral reef becomes narrower and shallower on approach towards the peripheral sea. The reef types may then alter from barrier reefs to fringing reefs. 3. The same geographical variation in coral reefs can also be expected on scattered islands from 30°N to 30°S and on completely drowned islands fringed by shelves in an open ocean. However, the reef type should be represented as an encircled reef like an atoll in this case. The postulated model has been tested by using larger scale charts and by measurement of certain of the morphological properties of coral reefs such as Rw, Rd, Sw, Sd, Ldmax, and the number of knolls and pinnacles. The measured results are shown in Fig. 4 to Fig. 11 and Table 3. The postulated model is supported by the following evidence. A zone of coral reef formation during periods of low sea-level stands has been confirmed from the coincidence of each geographical range with an Rd of about 100 meters and a W-ratio of 100%. This is also substantiated by the fact that Rd is roughly equivalent to the thickness of Quaternary reef limestones related to sea level changes during the Quaternary period (Table 1). Seas which have permitted the formation of coral reefs even during periods of low stands of sea level, or glacial ages, are referred to as the "core zone". Seas which have expanded towards the north or south with subsequent rises in sea level constitute the "peripheral zone" (Fig. 15). The geographical variation in the thickness of reef limestones is demonstrated as an overall, systematic decrease in Rd from the core zone to the peripheral zone. The geographical variation in the width of coral reefs is demonstrated as a W-ratio of 100% in the core zone which shows a systematic decrease towards the peripheral zone. The geographical variation in reef types is also supported by the following findings. Barrier reefs and atolls center upon the core zone, while fringing reefs and apron reefs center upon the peripheral zone. Furthermore, the most frequent depths of Rd for each reef type are equivalent to the Rd of each zone, i.e. the Rd of barrier reefs and atolls coincides with that of the core zone, while the Rd of fringing reefs and apron reefs coincides with that of the peripheral zone (Fig. 14). The geographical variation of the knolls and pinnacles in lagoons is roughly as follows. Most knolls center upon the core zone, while the range of pinnacles shows a wider distribution than that of the knolls. However, more specific and precise data are required on this subject. The postulated model is also supported by the linear relationship, Rw/Rd=Sw/Sd (Fig. 12), and can be redrawn schematically as in Fig. 16. The growth rate ofa coral reef (Table 2) may possibly follow and approach the rate of sea level changes occurring throughout the Quaternary period. The amount and the rate of crustal movement (Fig. 13) appear to have almost no bearing on the explanation of the global distribution of coral reefs. The present geomorphology of coral reefs must be based on karst topographies which have been eroded by subaerial solution. Therefore, Ldmax must be carefully evaluated. The proposed model effectively explains the geographical variation of coral reefs which have formed during the Quaternary period. However, explanations of the geographical distribution of coral reefs since the Tertiary or the Mesozoic also require a consideration of the regional plate tectonics, as indicated by Newell (1972) and Hori (1974).