In the current research work, we present an improvement of meshlessboundary element method (MBEM) based on the shape functions of radialbasis functions-QR (RBF-QR) for solving the two-dimensionalelasticity problems. The MBEM has benefits of the boundary integralequations (BIEs) to reduce the dimension of problem and themeshless attributes of moving least squares (MLS) approximations.Since the MLS shape functions don't have the deltafunction property, applying boundary conditions is not simple. Here, wepropose the MBEM using RBF-QR to increase the accuracy andefficiency of MBEM. To show the performance of the new technique,the two-dimensional elasticity problems have been selected. We solvethe mentioned model on several irregular domains and report simulation results.