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Based on element-free Galerkin (EFG) method and the complex variable moving least-squares (CVMLS) approximation, the complex variable element-free Galerkin (CVEFG) method for two-dimensional elasticity problems is presented in this paper. With the CVMLS approximation, the trial function of a two-dimensional problem is formed with a one-dimensional basis function. The number of unknown coefficients in the trial function of the CVMLS approximation is less than in the trial function of moving least-squares (MLS) approximation, and we can thus select fewer nodes in the meshless method that is formed from the CVMLS approximation than are required in the meshless method of the MLS approximation with no loss of precision. The formulae of the CVEFG method for two-dimensional elasticity problems is obtained. Compared with the conventional meshless method, the CVEFG method has a greater precision and computational efficiency. For the purposes of demonstration, some selected numerical examples are solved using the CVEFG method.

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