A non-destructive method for determining the properties of laminated composite materials made of twill-weave glass fibre fabric is considered. To determine the elastic characteristics of the composite monolayer, a combined numerical–experimental method is used. The method combines the results of experimental tests and numerical modelling methods using optimization techniques. Firstly, 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 frequency response are evaluated using Analysis of Variance (ANOVA). Using the results obtained, the properties of the elastic characteristics of layered composite plates made of twill-weave glass fibre fabric using vacuum infusion are determined. To compare the properties obtained from the dynamic calculation, a series of static measurements of tensile samples were carried out. The results showed that the elastic modulus from the static test and the flexural test do not coincide by 4% and 23%, respectively. The technique demonstrates high accuracy and applicability for the non-destructive determination of dynamic material properties in engineering practice.