Interval analysis method on critical speeds and steady response was established to acquire accurate results with the bounds of parameters based on Chebyshev expansion. Critical speeds were expressed as Chebyshev polynomials expansion to calculate the interval results when support stiffness

density or elastic modulus were interval parameters. The comparison between Chebyshev method

perturbation method and combination method illustrated that the maximum error was less than 0.07%. The Chebyshev method on steady response was proposed while modal superposition was applied to correct the bounds. The defect of the original method arising from the large uncertainty of critical speeds was fixed. The comparison with Monte Carlo method illustrated that the maximum error of response upper bound was less than 8%. The differential equations of the original system do not need to be modified in Chebyshev method. The results illustrate that combined with commercial finite element software

the method has good applicability and advantages of high accuracy.