Real composite materials such as concrete, mortar, etc. sometimes contain unintended voids in itself. The voids govern the macro brittle behavior due to the micro cracks. We propose a special element containing a micro void, namely BE-FE blending element. The displacement inside the element is represented by a superposition of the accurate solution from boundary element method and the continuous shape functions. The stiffness matrix implicitly accounts for the the effects from the void, and is applied to the stiffness matrix of conventional finite element method. The accracy of the stress fields is gurannteed when the void size is less than 10% of the element size. We exhibits the applicabliity to the deformation analysis for the extention of elastic plate with a single void, multiple voids and also a inclusion.