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• The open crack in a hollow shaft is modeled based on relationships between crack depth and shaft radii. • The surrogate function for the uncertain dynamic response is established using the interval descriptions. • The accuracy and robustness of the interval methodology are validated by traditional sampling methods. • The nonlinear dynamics are analyzed considering various uncertain parameters with different variations. This paper focuses on the vibration behaviors of a hollow-shaft rotor system in presence of an open crack under inherent model uncertainties. Non-probabilistic interval variables are used to represent the uncertain parameters, which releases the high demands of probabilistic knowledge in the traditional methods. In modeling the shaft, local stiffness matrix of the cracked element is derived by using the neutral axis method. The periodic response of the rotor system is solved by combination of the finite element method (FEM) and the harmonic balance method (HBM). A simple mathematical function, termed as the uncertain response surrogate function (URSF), is constructed to estimate the vibrational response in various cases where different parametric uncertainties are taken into consideration. In order to verify the robustness and accuracy of the URSF, the bounds of estimated response are compared with those obtained from the classical methods. Results show that the surrogate function has good accuracy and robustness, providing an effective method and guidance for diagnosing crack in uncertain context. [ABSTRACT FROM AUTHOR]