Abstract
In the present paper, we investigated the exact solution of unsteady motion of micropolar fluid in the half-plane when the shear stresses are given on the boundary. The Laplace-Fourier transform technique is used to point out the exact solution in two-dimension of unsteady micropolar fluid under influence of magnetic field. Numerical results of the physical quantities such as tangential and normal velocities, pressure, microrotation, stresses and momentums are obtained and presented graphically. The problem could be met in the study of the flow near a solid boundary which is not wet by the given fluid.