The efficient monetary system requires that the money supply is flexible enough，in order to face the change of the money demand. If the money supply can not be changed while there is a sustained increase in the money demand, it will produce a shortage of money. This paper, based on a simple cash-in-advance model, studies the monetary system of the Song Dynasty, and expects to analyze the intrinsic reason of the money shortage prevailing in the Song Dynasty. Chinese ancient copper coins system does have its particularity, because every dynasty only issued one kind of copper coin officially. Due to the need to avoid the price of its generally accepted coin below par value， it is impossible to issue the debased coin successfully. The weight of the coin each dynasty repeatedly cast was 30 kilogram without much deviation, fineness also remained in roughly 60% to 80%, and this standard was kept all the time. The official debasement would face many difficulties. Even the newly established Dynasty cannot ignore the habit of the people. At the same time, because of the huge stock of the copper coin in folk, casting debased coins was almost impossible. Even if the government made the law that the debased coins would be valued one wen, in response, the folk would appreciate the old coins to the maximum. The coin system of Song Dynasty is the representative of ancient Chinese coin system. According to Cipolla and Sargent's researches, before the establishment of the modern monetary systemt he only way to increase the supply of small denomination coins was to reduce the cost of production. And before the first industrial revolution, the only way to reduce the production cost of the coins was to increase the proportion of base metals in the coin. In the single metal copper coinage, copper coin is in fact the only official issued currency. And it is in fact the only generally accepted currency. The yield of the copper coin is maximum increment of the money supply every year, and copper coins stock can also be regarded as the stock of money. So given technical conditions, and there is not the possibility of debasement, if there is no decline in copper prices, the increase in the money supply will be impossible without a cost-rising. So the fundamental cause of the long time shortage of copper coins from middle Tang Dynasty was the ancient Chinese copper coin system that used the base metal copper as the money material. According to the mainstream research, the primary cause of money shortage in Northern Song Dynasty was the behaviors of reducing money supply, such as coins melting, outflow of coins, and coins hoarding. Scholars argue that the low value of copper coins led to the occurrence of such behaviors. Different from the previous studies, this paper have found that the single metal copper coinage is the essential cause of the shortage of money in the Northern Song Dynasty. And the high production cost of the coin which was caused by the backward technology of copper mining and coinage, made the Northern Song government money supply ability limited, and therefore the money supply cannot be enough to satisfy the growing demand for the currency in Northern Song Dynasty. These were the manifestation of the essential cause proposed. Each dynasty`s policymakers tried to solve the problem of the shortage of money supply, by casting iron money, issuing notes and the use of precious metals as media of exchange, etc. to break the single metal copper coinage, but the effect is limited.  In fact, there were great innovations in the management thought and practice of paper money in the Southern Song Dynasty. The expansion of overseas trade made the government wealthier, and made the precious metals stock increased. Also, it gave the economy of the Southern Song Dynasty new stimulus, enable the authorities to realize the diversification of sources of wealth and produce a preliminary mercantilism. But the war between the Southern Song and the barbarian, barbarian government`s arbitrary monetary management and the suppressing of business class in the first Ming Dynasty emperor interrupted the evolution.