In the published line-spring boundary element method, the effect of bending is not considered. Therefore it cannot be used to deal with the problem of a surface cracked plate. Taking the advantage of the line-spring model and the boundary element method the authors present a new line-spring boundary element method in which the effect of membrane force and bending moment in a Reissner plate is taken into account. The implementation of the method is discussed in detail. The stress intensity factors for several example problems concerning surface cracked plates are calculated. Comparisons are made with the Newman-Raju solutions. The results show that the proposed method is efficient.