Due to the engine’s start/stop system and a sudden increase in speed or load, the development of alloys suitable for engine bearings requires excellent tribological properties and high mechanical properties. Including additional elements in the Al-rich matrix of these anti-friction alloys should strengthen their tribological properties. The novelty of this work is in constructing a suitable artificial neural network (ANN) architecture for highly accurate modeling and prediction of the mechanical properties of the bearing aluminum-based alloys and thus optimizing the chemical composition for high mechanical properties. In addition, the study points out the impact of soft and more solid phases on the mechanical properties of these alloys. For this purpose, a huge number of alloys (198 alloys) with different chemical compositions combined from Sn, Pb, Cu, Mg, Zn, Si, Ni, Bi, Ti, Mn, Fe, and Al) were cast, annealed, and tested for determining their mechanical properties. The annealed sample microstructure analysis revealed the formation of soft structural inclusions (Sn-rich, Sn-Pb, and Pb-Sn phases) and solid phase inclusions (strengthened phase, Al2Cu). The mechanical properties of ultimate tensile strength (σu), Brinell hardness (HB), and elongation to failure (δ) were used as control responses for constructing the ANN network. The constructed network was optimized by attempting different network architecture designs to reach minimal errors. Besides the excellent tribological characteristics of the designed set of alloys, soft inclusions based on Sn and Pb and solid-phase Cu inclusions fulfilled the necessary level of mechanical properties for anti-friction alloys; the maximum mechanical properties reached were: σu = 197 ± 7 MPa, HB = 77 ± 4, and δ = 20.3 ± 1.0%. The optimal ANN architecture with the lowest errors (correlation coefficient (R) = 0.94, root mean square error (RMSE) = 3.5, and average actual relative error (AARE) = 1.0%) had two hidden layers with 20 neurons. The model was validated by additional experiments, and the characteristics of the new alloys were accurately predicted with a low level of errors: R ≥ 0.97, RMSE = 1–2.65, and AARE ˂ 10%.