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An interval element-free Galerkin method was proposed to solve some issues in structural design and analysis of structural parameters that have errors or uncertainties caused by manufacture, installation, measurement, or computation. Based on the interval mathematics and perturbation theory, we deduced interval element-free Galerkin method equilibrium equations using the element-free Galerkin method and solved them using the parameter perturbation of interval number. A bar under uniform load, a bi-material cantilever beam subjected to uniform stress, and collinear double edged cracked plate subjected to uniform tensile stress, including uncertainty parameters, were analyzed. Numerical simulations show that interval element-free Galerkin method is accurate and effective in solving the uncertainty problems.