The results of an investigation into the barrier and mechanical properties of polymer nanocomposites prepared by blending a styrene-acrylate copolymer solution with a suspension of organically modified montmorillonite are presented. Data on the influence of montmorillonite clay content on the tensile stress–strain curves, elastic modulus, strength, and ultimate elongation of the nanocomposites are obtained. The influence of montmorillonite content on the barrier properties of the nanocomposite is investigated with the example of water vapor permeability. The experimental values of the permeability coefficient are compared with those calculated by using a model taking into account the increased path of diffusing water molecules caused by the shielding effect of plate like particles.