The bending problem of the face polymethacrylimide（PMI） foam core sandwich beam was taken as the plane stress problem and the differential equation of bending deformation for aluminum face PMI foam core sandwich beam was established by elasticity theory. The deflection expressions of bending deformation for the bending of aluminum face PMI foam core sandwich beam were derived from taking the external load on the beam as distributed load by singular functions. According to the deduced deflection expressions, the midpoint deflections of the aluminum face PMI foam core sandwich beam were calculated, with the results closer to the experimental results compared with the calculation results by the energy method and the finite element method and the test results in some other related references. It is proved that the accuracy of this method is high. Furthermore, the general formula of bend deflection for aluminum faces PMI foam core sandwich beams is given and the calculation formula of deflection is simple which can be applied to the practical engineering.