The influence of the gravity and interface kinetics on interface shape and interfacial concentration distribution was numerically investigated by using Galerkin finite element method. A boundary mapping technique was used for dealing with free boundary problem. A two-dimensional steady-state model of TGS crystal growth was developed. The results show that with the increase of the gravity level, the growth rate becomes faster, the growth face becomes more curved and interfacial concentration distribution more non-uniform. The consideration of interface kinetics will cause the decrease of growth rate as compared with the pure transport model. It seems that the interface shape does not change very much within two cases of k = 5.7 cm4/(mol·s) and k = ∞, but its position does.