Based on Eringen's Micropolar Elasticity Theory (MET) and Smith's displacement assumption, a finite element formulation is derived and a computer program is developed to solve the Micropolar torsion problems. The numerical results are first obtained for a solid cylinder, and shown to be in excellent agreement with existing MET analytical solution. Next, the new formulation is applied to solve, for the first time, the torsional problems in a hollow cylinder. The effects of coupling factor and radius ratio on the micropolar effects are studied.