The complex function method was used in the solution of micropolar elasticity theory around cavity in an infinite elasticity plane. In complex plane, the general solution of two dimension micropolar elasticity theory is given. The solution comes from analytic function and "Zonal Function". The boundary conditions of non-circular cavity are satisfied by using the conformal mapping method. Based on the method, a general approach solving the stress concentration in micropolar elasticity theory is established. Finally, the numerical calculation is carried out to the stress concentration coefficient of circular cavity.