 This paper examines the dynamic characteristics of a composite beam with uncertain design parameters. The authors use interval analysis to analyze the behavior of the beam using the fractional Zener model, which describes the behavior of both elastic and viscoelastic layers. They then compare the results of the analysis to the actual behavior of the beam by using the vertex method, which is a comparative method that approximates the lower and upper bounds of the dynamic characteristics using the first and second order Taylor series expansion. Additionally, they describe an algorithm for determining the critical combination of uncertain design parameters. Finally, numerical examples demonstrate the effectiveness of these methods and their applicability to structures with many uncertain parameters and high uncertainties. This article was authored by Magdalena Lesecaplura.