Rotation of particles in granular material is an important mechanism, which is responsible for the distinct feature of moment transfer within granular material. A couple-stress continuum is adopted to model such effect. The paper presents a mix-mode finite element formulation for the analysis of a couple stress continuum. A modified variational formulation is proposed to render unconditional convergence. The developed finite element method is validated by comparing the computed results with closed-form solutions. In order to verify whether the couple-stress continuum is appropriate for modeling granular media, finite element results for two different boundary value problems are performed and compared with that obtained from discrete analysis. Physical meaning of internal length, a new parameter of the material, is discussed. The suitability of the couple-stress continuum for modeling granular medium is evaluated.