One of the most important characteristics of structural materials is their stiffness. Ensuring the required stiffness is the key to durability and efficient operation of the structure. Variation in the compositions of polymer composite materials (PCM), the introduction of various additives and modifiers into their structure leads to changes not only in the operational properties of composites, but also in their stiffness. Achieving a positive effect on a number of some properties can lead to the loss of others. This article describes the technology of forming polymer composite materials with a hybrid matrix. The peculiarity of these materials is that the hybrid matrix is formed by two materials, one of which (the main binder) is completely cured after molding, and the second retains its "liquid" state and represents a separate phase in the composite structure. Such PCM have a variable stiffness of material, which makes it necessary to experimentally study the effect of the quantity and location scheme of the "liquid" phase component on this indicator. The technology of the laboratory method for determining the stiffness of PCM samples is described, which consists in measuring the maximum deflection of a flat sample under the action of a statically applied load. The measurement was carried out on carbon fiber reinforced plastic samples with a hybrid matrix formed by an epoxy binder and a silicone elastomer. The influence of the amount and location scheme of silicone elastomer in the composite structure, as well as the scale effect on the maximum deflection was evaluated. The amount of silicone elastomer was taken in a total of 0.25 mL and 0.50 mL in all locations, varying the number of locations and their direction relative to the length of the sample. It was found that the longitudinal location of silicone elastomer in PCM samples leads to the greatest decrease in their rigidity. The amount of silicone elastomer in the location zone does not significantly affect the change in the stiffness of the samples. Increasing the number of layers of reinforcing fabric by 2 times allows to reduce the deflection of the test samples by 7–10 times depending on the applied load. Doubling the width of samples and silicone elastomer locations results in a 2-fold reduction in maximum deflection. With an increase in the thickness of PCM in samples with silicone elastomer, the values of maximum deflection under the action of various statically applied loads are similar to the values of this parameter of carbon fibers of the same thickness without a component of the "liquid" phase.