Analysis of a structure is a crucial procedure to ensure its reliable design and performance. Because of complexities present in the closed-form structural analysis methods, numerical schemes have become the standard of practice. These schemes are generally performed deterministically. However, the input parameters defining the material and geometric properties may possess uncertainties. They can arise from various sources including modeling, manufacturing, and construction errors. The quantification of uncertainties is generally based on either probability theories (using random variables) or possibility theories (using interval and fuzzy variables). In this work, the finite-element-based probabilistic and possibilistic methods are discussed and compared. A case study of static and dynamic uncertainty analyses of a structure using the aforementioned schemes is performed. The results of those analyses suggest that the incorporation of uncertainty in the analysis provides a higher level of confidence. Moreover, they are compared for both accuracy and computational efficiency. Based on the results, it is observed that the determination of approach must be based on the problem complexity as well as the level of available information.