The use of composite materials instead of conventional ones allows a significant reduction of product weight without deteriorating strength characteristics, which is particularly important for aviation and aerospace industry. This paper deals with the research of physical and mechanical characteristics of nano-modified epoxy composite materials. Polymer materials often do not possess sufficient rigidity and strength to satisfy requirements to various structures made of these materials. Insertion of various reinforcing fillers is a conventional method of improving these properties so that filled polymers could be used as structural materials. The goal of this study is to develop a method of epoxy resin binder modification by silicon dioxide nanoparticles and a technology of obtaining the corresponding composite materials with improved performance. Changes of Young’s modulus and modulus of rupture according to the order of the filler insertion are investigated. A series of experiments is conducted to study the effect of filler particles size on composites materials fracture.