This paper presents a technique to establish the strain incremental formulation in the boundary element method applied to elastoplasticity problem. In this technique, the application of second order singularity problem is avoided, and only first order singularity problem is sufficient. The proposed technique is applied to analyse a timber beam structure at the plastic stage. The solution is compared with existing strain formulation method proposed by established publication. The result gives an improved solution compared with the existing method. The proposed technique is a simplified formulation where there is no second order singularity involved in the formulation.