Elastic electrically conductive composites with an ethylene octene copolymer matrix (EOC) and vapor-grown carbon fibers (VGCF) were prepared by ultrasonication in a toluene solution, and their morphology, mechanical and electrical properties were also evaluated. EOC/CF composites were estimated for their mechanical and viscoelastic properties. The morphology of the composites was analyzed using scanning electron microscopy (SEM), and stress–strain curves were generated to measure the stress and tensile modulus of the composites. The experimental results were compared with various theoretical models, including the Burgers model, which separates viscoelastic behavior into several components. A dynamic mechanical analysis was also used to measure the composites’ storage modulus, loss modulus, and damping factor at different frequencies. The composites’ complex viscosity and storage modulus were increased with higher wt.% of CF, which enhances the elastic response. Electrical resistivity measurements were conducted on the composites and it was found that the resistivity decreased as the sample was loaded and increased as it was unloaded. Overall, the study provides insights into the mechanical and viscoelastic properties of EOC/CF composites, which could be helpful in developing sensors such as pressure/strain sensors.