The investigation of two-dimensional magnetic fluid flow is necessary and important in order to examine the fundamental characteristics of a magnetic fluid. In the present paper, the flow in a square cavity, filled with a magnetic fluid, to which a magnetic field is applied parallel to the moving wall, is numerically analyzed by the finite element method on the basis of governing equations for magnetic fluids with internal rotation. The effects of a magnetic field and some dimensionless parameters characterizing magnetic fluid flow are discussed in detail. The results obtained here are as follows : (1) The GSMAC method has been developed for magnetic fluid algorithm in a homogeneous magnetic field. (2) The flow remarkably expresses a non-Newtonian property due to the micropolar effect when the magnetic field is not applied. (3) When a moderate magnetic field is applied, the flow of the magnetic fluid is similar to that of a Newtonian fluid.