The so-called squeeze flow involves a magnetorheological (MR) fluid sandwiched between two planar surfaces setting up a flow channel. The height of the channel varies according to a prescribed displacement or force profile. When exposed to a magnetic field of sufficient strength MR fluids develop a yield stress. In squeeze-mode devices the yield stress varies with both the magnetic field magnitude and the channel height. In this paper an unsteady flow model of an MR fluid in squeeze mode is proposed. The model is developed in Ansys Fluent R16. The MR material flow model is based on the apparent viscosity approach. In order to investigate the material's behaviour the authors prepared a model of an idealized squeeze-mode damper in which the fluid flow is enforced by varying the height of the channel. Using mesh animation, the model plate is excited, and as the mesh moves, the fluid is squeezed out of the gap. In the simulations the model is subjected to a range of displacement inputs of frequencies from 10 to 20 Hz, and local yield stress levels up to 30 kPa. The results are presented in the form of time histories of the normal force on the squeezing plate and loops of force vs. displacement (velocity).