Several methods are presented for the modeling and analysis of uncertain beams and other structural elements/systems. By representing each uncertain parameter as an interval number, the vibration problem associated with any uncertain system can be expressed in the form of a system of nonlinear interval equations. The resulting equations can be solved using the exact or a truncation-based interval analysis method. An universal grey number-based approach and an interval-discretization method are proposed to obtain more efficient and/or more accurate solutions. Specifically, the problem of the coupled bending-torsional vibration of a beam involving uncertainties is considered. It is found that the range of the solution (response) increases with increasing levels of uncertainty in all the methods. Numerical examples are presented to illustrate the computational aspects of the methods presented and also to indicate the high accuracy of the interval-discretization approach in finding the solution of practical uncertain systems. The results given by the different interval analysis methods (including the universal grey number-based analysis) are compared with those given by the Monte Carlo method (probabilistic approach) and the results are found to be in good agreement with those given by the interval analysis-based methods for similar data.