Two parallel infinite plane disks, between which is contained a viscous fluid, oscillate torsionally about a common axis. Of specific interest are the cases where (i) one disk only is in motion, and (ii) the disks oscillate 180° out of phase, but with the same frequency and amplitude. The basic parameter is found to be the Reynolds number derived from the frequency, the kinematic viscosity and the disk separation. Solutions of the Navier-Stokes equations for both small and large Reynolds numbers are developed and the transverse and radial-axial flows investigated.