Abstract: In order to increase the computational efficiency of the interval eigenvalues, the monotone property of the design parameters of the structure matrix is studied firstly. Then a fast methodology for calculating the eigenvalues of structure matrix with interval parameters is put forward, which is based on the Rayleigh quotient and the theories of the interval mathematics. As the deviation of the interval factors of the design parameters are similar and close to unity, it shows that the computational error of the fast methodology are determined by the dispersion between the interval factors, and the error come up to zero if all the interval factors are equal. Finally, two numerical examples are given, which proves that the presented method is more feasible and efficient than the global optimization algorithm and the interval stepped dividing method for engineering applications.