The purpose of this study is to present a parametric analysis of how the fiber orientation angle affects elastic wave dispersion relations in the case of the CARALL composite. The CARALL composite is made up of multiple plies of carbon fiber and aluminum plies bonded together. The material consists of 14 layers, where the layers are constructed from aluminum alloy and carbon/epoxy resin fibers. The overall configuration of the CARALL composite is [Al, θ5, Al]s, where the angle parameter is varied between 0° and 90°. The stiffness matrix approach is used to determine the dispersion curves, and the “Dispersion Calculator” computer program is employed in the analysis. The results indicate that the difference in fiber orientation angle significantly affects the shift in phase velocity between the primary symmetric mode and the horizontal shear mode. However, the sensitivity of the other modes to the angle is negligible. This study provides valuable insights into the impact of fiber orientation angle on elastic wave dispersion relations in CARALL composites and could inform future research on composite material design and optimization.