As an example of the La-Mg-Y system, the method how to set up the thermodynamic model of individual phases was introduced in the process of thermodynamic optimization. The solution phases (liquid, body-centered cubic, face-centered cubic, hexagonal close-packed and double hexagonal close-packed) were modeled with the Redlich-Kister equation. The compound energy model has been used to describe the thermodynamic functions of the intermetallic compounds in the La-Mg-Y systems. The compounds Mg 2 Y, Mg 24 Y 5 , Mg 12 La, Mg 17 La 2 , Mg 41 La 5 , Mg 3 La and Mg 2 La in the La-Mg-Y system were treated as the formulae (Mg, Y) 2 (La, Mg, Y), Mg 24 (La,Mg,Y) 4 Y, Mg 12 (La,Y), Mg 17 (La,Y) 2 , Mg 41 (La,Y) 5 , Mg 3 (La,Mg,Y) and Mg 2 (La, Y), respectively. A model (La,Mg,Y) 0.5 (La,Mg,Y) 0.5 was applied to describe the compound MgM formed by MgLa and MgY in order to cope with the order-disorder transition between body-centered cubic solution (A2) and MgM with CsCl-type structure (B2) in the La-Mg-Y system. The Gibbs energies of individual phases were optimized in the La-Mg, La-Y and La-Mg-Y systems by CALPHAD technique. The projection of the liquidus surfaces for the La-Mg-Y system was predicted. The Mg-based alloys database including 36 binary and 15 ternary systems formed by Mg, Al, Cu, Ni, Mn, Zn and rare earth elements was set up in SGTE standard.