This paper develops a linear theory for the analysis of beams based on the micropolar continuum mechanics. Power series expansions for the axial displacement and micro-rotation fields are assumed. The governing equations are derived by integrating the momentum and moment of momentum equations in the micropolar continuum theory. Then, the deformation of a cantilever beam with transverse concentrated tip loading has been studied. This paper also develops a new smoothed finite method (SFEM) based on the couple stress theory using the triangular meshes. We first construct a generalized energy functional for the linear couple stress elasticity, and use a penalty function technique to release the geometric constraints of micro-body rotation, which ensure this procedure does not increase the extra unknown variables. Then we develop a SFEM formulation with C0-continuity satisfying the generalized energy consistency conditions to guarantee the convergence. Some numerical experiments verify the results from the theoretical analysis.