Thermodynamic models for molecular-beam epitaxy(MBE) growth of ternary Ⅲ-Ⅴ semiconductor materials are proposed.These models are in agreement with our experimental materials InGaP/GaAs and InGaAs/InP,and reported GaAsP/GaAs and InAsP/InP in thermodynamic growth.The lattice strain energy △G and thermal decomposition sensitive to growth temperature are demonstrated in the models simultaneously.△G is the function of the alloy composition,which is affected by flux ratio and growth temperature directly.The calculation results reveal that flux ratio and growth temperature mainly influence the growth process.Thermodynamic model of quaternary InGaAsP/GaAs semiconductor material is discussed also.