Many American universities have REU Summer programs. My perception is that when an university opens REU positions, these are aimed at the given university's students. Some universities allow students from other American universities to apply.

The good news is that Caltech has the wonderful <a href="http://www.surf.caltech.edu">Summer Undergraduate Research Fellowship</a> (SURF) program, which is open to students from non-American universities. Many of the international students at SURF are from Cambridge University, for example. I am enormously fortunate to have had the privilege to attend SURF a few years ago. It was the best Summer of my life. I highly recommend it! 

I don't know what kind of Mathematics is being done at Caltech right now, but if you find some professor doing work that interests you, you can always send him an email with your CV explaining why you would like to work with him, and asking whether he will have SURF students in Summer 2011. Even if he will not, he might inform you of some colleague of his who will. The application deadline is around late February / early March 2011, I believe.The stipend is quite generous, in my opinion.