Abstract: In the paper, after studying literatures on the eccentric annular flowing of power-fluid in the pipes, it is not on speaking terms that those are computed approximately. According to N-S equations of hydromechanics and mechanics, the interface-coupling equations on eccentric annular flowing of power-fluid in the pipes are scientifically and strictly put forward, and a system of partial differential equations describing the flow is obtained. By numerical computing, the important flowing laws on eccentric annular flowing of power-fluid are obtained and it is very important to oil industry.