Abstract: Conventional collocation meshless methods suffer from instability, poor accuracy and high-order derivation problems in the solution processes. The least square mixed collocation method based on the Euler interpolation is proposed in this study to overcome the above problems. Both the displacement and the strain are unknowns, the derivatives of which are expressed by using the Euler interpolation. The Gaussian weight function is introduced, resulting in over-determined systems. The over-determined systems are to be solved subjected to boundary conditions in terms of stress and displacement. This proposed method does not require domain integration, which is essentially truly meshless. Typical examples of plane elastic problems are used to demonstrate the high accuracy of the method.