Abstract The singular boundary method (SBM) belongs to the family of meshless boundary collocation methods and can be viewed as one kind of modified method of fundamental solutions (MFS). This method was originally proposed in 2009, based on the notion of boundary element method (BEM) and MFS, fully inherits the merits of both and in the meantime possessing its unique advantages. The key idea is to introduce the concept of the origin intensity factor to isolate the singularity of the fundamental solutions, so that the source points can be directly placed on the real boundary. This overcomes a perplexing fictitious boundary outside physical domain in the MFS. This paper makes the first attempt to apply the method to two dimensional elasticity problems. The accuracy and stability of the proposed method are tested to three benchmark elasticity examples in which the SBM solutions are compared with the results obtained by using the MFS, traditional SBM, and the finite element method (FEM).