A systematic and rational approach is presented for the consideration of uncertainty in rotordynamics systems, i.e. in rotor mass and gyroscopic matrices, stiffness matrix, and bearing coefficients. The approach is based on the nonparametric stochastic modeling technique which permits the consideration of both data and modeling uncertainty. The former is induced by a lack of exact knowledge of properties such as density, Young's modulus, etc. The latter occurs in the generation of the computational model from the physical structure as some of its features are invariably ignored, e.g. small anisotropics, or approximately represented, e.g. detailed meshing of gears. The nonparametric stochastic modeling approach, which is briefly reviewed first, introduces uncertainty in reduced order models through the randomization of their system matrices (e.g. stiffness, mass, and damping matrices of nonrotating structural dynamic systems). Here, this methodology is first extended to permit the consideration of uncertainty in symmetric and asymmetric rotor dynamic systems. Its application is next demonstrated on a symmetric rotor on linear bearings and uncertainties on the rotor stiffness (stiffness matrix) and/or mass properties (mass and gyroscopic matrices) are introduced that maintain the symmetry of the rotor. The effects of these uncertainties on the Campbell diagram, damping ratios, mode shapes, forced unbalance response, and oil whip instability threshold are analyzed. The generalization of these concepts to uncertainty in the bearing coefficients is achieved next. Finally, the consideration of uncertainty in asymmetric rotors is addressed and exemplified.