Abstract The phase equilibria between β(bcc), α(hcp), Ti 3Al-α 2(hcp) and Ti 5Si 3(hcp) in the Ti-Al-Si system have been investigated in the temperature range of 700 to 1200°C. Isothermal sections of the ternary phase diagram have been assessed employing thermodynamic software, which uses the compound-energy model to describe mathematically the phase. Available experimental phase equilibria results on the Ti-Al-Si system were used to calculate missing binary and ternary interaction parameters and assess isothermal phase diagrams. Extrapolations in the resulting tie-triangles indicate the existence of three eutectoid reactions in the Ti-rich corner of the ternary diagram: β−⪢ α+ Ti 5 Si 3, α−⪢ α 2+ Ti 5 Si 3 and β−⪢ α 2+ Ti 5 Si 3. Additionally, extrapolations in the β+ α 2+ α tie-triangle observed at 1100°C indicate that two possibilities arise to represent a peritectoid reaction involving α, β and α 2 phases: β+ α 2−⪢ α and β+ α−⪢ α 2, depending on the alloy composition and on the effect of temperature on the solubility of Si in α phase.