In order to solve the problem that some structural parameters have errors or uncertainties which are caused by manufacture, installation, measurement or computation in structural analysis and design, an interval local orthogonal element-free Galerkin method(ILOEFGM）is proposed. Based on the interval mathematics, inner product space, perturbation theory, element-free Galerkin method(EFGM）are employed to deduce ILOEFGM equilibrium equations, and the parameter perturbation of interval number is used to solve the ILOEFGM equilibrium equations. As an application of the method, a numerical example based on the problem for plane with cracks is given. The calculated results show that the method is effective.