Parametric uncertainties are present in complex mechanical systems due to various reasons such as material dispersion and wear. This paper investigates the effects of interval uncertain parameters on the dynamic behaviors of a rotor system with a transverse breathing crack in the shaft. The uncertainties are modeled as uncertain-but-bounded interval inputs on the basis that no sufficient prior information is available to define their precise probabilistic distributions. A finite element rotor model is formulated and the harmonic balance method (HBM) is employed to solve the deterministic dynamic problem. Based on the Chebyshev approximation theory, a surrogate model for the uncertain problem is established and then used to determine the bounds of the nonlinear dynamic responses. The accuracy verification is performed by comparing with the scanning method. Simulations are carried out considering different uncertainties with several uncertain degrees. It will provide some references for early crack fault detection and condition monitoring in rotor systems with uncertainties included.