The paper considers a non-destructive method for determining the properties of composite layered materials made of twill-woven glass fabric. A combined numerical–experimental method is used to determine the elastic characteristics of a composite monolayer. The method combines the results of experimental tests and numerical modeling methods using optimization techniques. At the first stage, the method for determining the properties is tested in a virtual experiment to determine the influence of the elastic characteristics of the material that do not affect the frequency response. The adequacy of the approximation equations and the influence of elastic constants on the frequency response are evaluated using Analysis of Variance (ANOVA). Using the results obtained, the properties of the elastic characteristics of composite layered plates made of twill-woven glass fabric using vacuum infusion are determined. To confirm the properties obtained from the dynamic calculation, a series of static tensile measurements of the samples was carried out. The results show that the method allows the elastic properties of the material to be determined with a deviation of about 5% compared to static tests, which is negligible compared to the advantages of the experimental modal analysis method. The technique demonstrates high accuracy and applicability for non-destructive determination of material properties in engineering practice.