Abstract: The mathematical characteristics of six growth equations and the theoretical basis of these equations applied to model stands diameter structure are analyzed and explored, and the long term observation data of permanent sample plots of Chinese fir are sorted out. The six equations are used to simulate stands cumulative diameter distribution, in order to clearly master the simulation parameters of every equation and what properties growth eqations have when used in the field of diameter structure. The results show: Richards equation at most time presents as a kind of Logistic and Weibull equation has its inflection point; except for Mitscherlich function, modelling precision of all growth functions are very high; the optimum seeking rate of Richards, Weibull, Logistic, Gompertz, Mitscherlich and Korf successively get down; the whole precision of Richards, Logistic, Weibull, Gompertz, Korf and Mitscherlich successively get down; the functions, relative growth rate of which is the index of variable,have the higher precision than those that relative growth rate is the power of variable; equations with three parameters have the higher precision than equations with two.