help - sharing file system among servers

[aj216]

Hi,

i need a file system to share among server A & B. do i need to have same user ids exists with same passwords, permissions on the file system in A & B server.
we want to avoid users connecting to server B to transfer/upload files into it.
what we are looking is having a common storage where user in Server A can place files and program in server B can access & process those files without user from server A actually connecting to server B.

suggestions or help is appreciated.