Prior to their surrender Japanese propaganda made claims that American soldiers would rape many Japanese women. I have no doubt that it did indeed happen, considering the nature of war and soldiers raping native women continues to the present, and by the existence of first person accounts of Americans raping Japanese women. But is there any study or analyses on how widespread it actually was? And did American censorship of Japanese media cover up American rapes of Japanese women?
The Japanese had, in the wake of the surrender, established a "volunteer association" of prostitutes called the Recreation and Amusement Association. Its purpose was essentially to be comfort women for the American, British, and Australian soldiers. The aristocracy wanted to protect their blue-blood daughters from what was percieved as lustful American occupiers, so they created this association-which had both women who believed they were protecting the bloodline of Japan as well as those who were essentially tricked into it-to help deter rape.
Dower noted in his Embracing Defeat that while the association existed, it was estimated that there were about 40 rapes or sexual assaults per day. Of course, there is a good chance that some of the rapes were originally consensual and were later called rape in an attempt to save face (due to certain xenophobic tendencies by the Japanese). However, undoubtedly there was enough public outcry that there were several demonstrations against the rapes by Japanese civilians. These demonstrations were cracked down on and the ringleaders were sometimes imprisoned. I recall reading about several Australians who were convicted of crimes while in occupied Japan: however the convictions were overturned by an Australian court due to insufficient evidence.
In any case, due to some outcry by moral leaders, the Occupation ordered the Recreation and Amusement Association to be shut down. After this, Dower notes that the rapes went from 40/day to 330/day. It should be noted that these rapes are only counted where the girl reported it to the police.
There were several court-martials for crimes committed during the occupation. But I don't really have any details on how effective these were, if someone has more details I'd appreciate it.
In any case, the rapes started to die down after 1946 as the Occupation became more established and there was a draw-down of troops. However, there were still occasional rapes now and then, especially in Okinawa which remained under US control for sometime. However, in the case of Okinawa, it should also be noted that the Imperial Japanese army defending Okinawa was far worse in their treatment of essentially their own civilians than the US military.
Source: Dower, Embracing Defeat