All Russian state medical schools do accept international applicants (with some special regulations for military schools).
The reputation of courses is a bit subjective thing. In MMA and RSMU they annually accept 600-900 new students for their Russian-medium program and up to 150 students for English-medium program. So, it may be 60 and 15 groups of students at the same year of study. It is obvious that nobody can provide you with the same level teacher/professor for every group. I believe it might be useful for you to consider relatively small medical schools (for instance Faculty of Medicine, Moscow State University and Faculty of Medicine, People Friendship University). However, an active student may satisfy his/her requirements at any good school.
To my experience, there is no official statistics on US residency placement of graduates of international medical schools. However, you may try to search for a information from ECFMG. Also, a couple of years ago it was a thread here about something like American Association of Gradates of Russian Med Schools (Russian doctors in the states). May be their internet-site contains some kind of info you are looking for.
It looks like two old problems for graduates of Rus med schools sitting for USMLE 20 years ago were: low level of English and no practice in sitting for MCT (almost tests and exams were oral). So, it was not the problem of knowledge. Currently, almost Russian university students do know English and the university developed new system of PC based tests. That is why we are starting to see more and more stories about successful transfer of Russian MD degree to western countries.
According to the MOE statistics in 2006/07 academic year 1539Americans got Russian student visas and started their study in Russian universities. Most part of them participated in short-term programs. However, in Moscow and St Petersburg you may meet a number of country mates taking their various graduate/postgraduate programs. Some of them are doing MD study.

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Contemporary Educational Programmes www.cep.ru

Mikhail, thanks very much.

Another quick question:

In the Russian medium programme, do the International students study alongside the Russian students in the same classes? Or is it a separate program and separate classes for the internationals?

Thanx buddy! This is a great post that shall help. Do you think St. Petersburg is a good school for MD and can I transfer my credits from another Russian University? Is St. Petersburg the port city of Russian? I mean the city just after Moscow?

kikhail, as per your information in Ryazan state medical university there is an english program for MD and it costs 3500 USD first year and from second to 6th year the cost per year is USD 2500. Am I right? Ow, that kool. I would like to join Ryazan then. Do I have to sit for entrance exams? Do I need to go for foundation course? I am from Bangladesh and whom do I contact for getting into Ryazan? Please reply and help. Thanx in advance.

oopSssssssssssss!!!!!!!!!!!!!!! sorry, i misspelled your name. Please don't mind that was a mistake.

Any website of Ryazan?

Traditionally, the groups in Russian medium program are mixed: international students are sitting together with local ones. Just sometimes, if some foreign students are still weak in Russian, they may get in a special group where teachers pay some more attention to the problem.

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Contemporary Educational Programmes www.cep.ru

The university in Ryazan granted duties of international office (in terms of the programs promotion and students recruitment) to a national company. This is how it works in Spain and some other countries. May be that is why there is no any internet site of the University to provide applicants with useful information about it. I know unofficial site kept probably by the students. It is in Russian and serves mainly to those who are already entered the University.
If you like a transfer there, you need to pass all the tests and exams during your study at the current university. However, I believe you may start your application now.
It looks like (if the transfer will be accepted) that you would need to leave Russia and come back with new student visa issued upon request of your new university.

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Contemporary Educational Programmes www.cep.ru