An extension of boundary element formulation for linear elasticity problems is presented. The standard formulation for planar problems uses two kernels. First kernel is used to obtain the displacement components on the boundary and has logarithmic singularity. Introducing a new artificial boundary this singularity has been eliminated. Second kernel is used to determine unknown stress component on the boundary and has 1/r singularity. Defining a new coordinate system, this singularity has been also eliminated. Numerical results for a sample problem are presented.