Clay soils are very useful as liners in geotechnical structures such as landfill sites, dams, water channels, etc. Swelling is a common problem in clay liners, however. To better understand swelling properties, in the present study clay nanocomposites were produced by means of the sol gel method, using a hydrophobic clay, polymers (locust bean gum, latex, glycerine, vinyl acrylic copolymer), and rubber powder. The study focused on the swelling and dynamic properties (secant shear modulus and damping ratio) of the clay nanocomposites researched experimentally in laboratory conditions. The dynamic tests were conducted on samples compacted using two different compaction energy levels. The test results were compared with those of natural clay and hydrophobic organo-clay. The test results revealed that the damping ratios and secant shear modulus of clay nanocomposites without rubber (CNC) and with rubber (CNCr) that were compacted with both the El and E2 energy levels were increased and decreased, respectively. In addition, with increasing percentage of vinyl acrylic in nanoclay composites, the secant shear modulus values were decreased and damping ratio values were increased. Consequently, the test results found that the swelling and dynamic properties of clay nanocomposites can be optimized in order to attenuate the negative effects of dynamic loads on clay liners.