In the present paper boundary value problems of three-dimensional micropolar theory of elasticity with constrained rotation are considered in thin region of the plate. On the basis of the previously developed hypotheses an applied theory of micropolar thin plates with constrained rotation is constructed, where transverse shear strains are taken into account. The energy balance equation is obtained and the corresponding variation functional is constructed. The finite element method is developed for the boundary problems (statics and natural oscillation) of micropolar plates with constrained rotation. On the basis of the analysis of the corresponding numerical results main properties of the micropolarity of the material are established.