The mechanical and rheological properties of a MR fluid depend on the induced microstructure of the imbedded ferrous particles. When subject to an external field these particles magnetize and align themselves in chains parallel to the applied magnetic field. The microstructure of these chains is a function of several parameters including particle size, applied magnetic field strength, and viscosity and velocity of the surrounding fluid. This thesis will create a model from a first principle approach to accurately predict the microstructure in a variety of different situations. The model investigated assumes the particles become magnetic dipoles upon the application of the magnetic field and that particle interaction is due solely to dipole-dipole interaction. Due to the inherently small size of the particles, drag is modeled using Stokes' drag. This mathematical model will be used to create a computer simulation to visualize and analyze the subsequent transient microstructures formed. The model will assume a constant magnetic field applied (IE no spatial or time gradients) and that the effects of this field are felt instantaneously.