I am from India. I was admitted to university A (no assistantship)
(among top 10 in USA) and I obtained visa for the same and entered
using I-20 of univ A. I also got an admit with graduate assistantship
from univ B (rank 30). I have the I-20 of univ B.
I have not registered at univ A. I want to shift to univ B now. I am
currently in USA. My current F1 visa is valid for 5 years.
My classes start at univ B on 20th of Aug. So I have to do processing
earlier than this.
Univ A would not transfer me to univ B before a semester.
What should I do now?

You must be registered with the univeristy which have initially
sponsered your I-20, in case you do not join university A, they can
refuse your transfer because you have not registered and started the
classes. In that case you will be "out of status", it had happend with
one of the students who came to us and he had to go back to india as
he was not keen to join the university which initially sponsered his
I-20.
good luck

vin