This paper deals with the periodic flow of a second-grade fluid caused by non-torsional oscillations of two disks rotating about non-coincident axes. While the two parallel disks are initially rotating with the same angular velocity about distinct axes, they start to execute non-torsional oscillations in their own planes and in the opposite directions. An exact solution is obtained for the components of the horizontal force per unit area exerted by the top and bottom disks on the fluid in the periodic state. The results are graphically displayed and the influence of the second-grade fluid parameter, the ratio of the frequency of oscillation to the angular velocity of the disks, the Reynolds number and the dimensionless velocity amplitudes of oscillation is discussed. It is observed that the change in the x-component of the mentioned force gets larger when the second-grade fluid parameter increases. However, an opposite effect is seen for the change in the y-component.