Abstract: The paper shows some of our recent developments in meshless methods. A new technique in meshless methods is given – the Interpolating Moving Least Square(IMLS)meshless method in square sphere. In the method, the technique of IMLS is adopted for the approximations of the unknown variable, and the square sphere for the geometric form of the local influence field. The adoption of these techniques presents the features of mesh free in which the nodes are placed and the numerical integration is performed without a mesh. It also satisfies the Dirichlet boundary condition. The method can be easily applied to nonlinear problems and heterosphere mechanics problems. Calculation results in two plane elastic mechanics examples show that the method has the advantages of excellent convergence rate, high accuracy and efficiency. It is very promising in engineering applications.