In this study, elastomer composites, including silicone rubber and barium titanate, were fabricated by mechanical mixing, a low-cost, fast, and easy technique to produce highly dielectric materials. The resulting composites were investigated in terms of their dielectric and mechanical properties in terms of filler percentage in the mixture. Dielectric permittivity measurements were taken using the microwave regime, and uniaxial tensile tests were carried out for the study of the materials’ mechanical properties, while combined experiments were also carried out to investigate potential correlations between them. The experimental results show that barium titanate inclusions in silicone matrix significantly improve the dielectric constant while reducing the mechanical properties of composites. In addition, combined experiments show that the composites exhibit a nearly stable dielectric profile under mechanical deformations. Consequently, mechanically mixed barium titanate–silicone elastomer composites could potentially become a cost-effective alternative in the extensive market for insulating materials and flexible electronics.