Abstract: To compute the statistical moments of the random response for mechanical structures subject to loads, material and geometry, a method was proposed. The basic random variables were discretized by the Chebyshev nodes to obtain discrete experimental samples. Then the Chebyshev approximation theory was applied to approximate the relationship of the random response-variables. The statistical moments of the random response were computed with the dimension-reduction method for multi-dimensional integration. Finally, a practical engineering case was used to demonstrate the generality and effectiveness of the proposed method.