Flow-induced vibrations of parallel plates in axial viscous flow were studied. Viscous flow theory was applied to describe the fluid-structure interaction. The fluid was supposed to be two-dimensional. The expressions of fluid velocities were created. The pressure grads were gotten with two-dimensional Navier-Stocks equations. Semi-analytical fluid pressures of a three-parallel plate-type structure were obtained. The added mass coefficients, added damping and added stiffness coefficients were determined. These analytical coefficients indicate a strong dependence on gap width.