The mathematical model of non-catalytic liquid-solid diffusion reactions discussed in this paper can be applied to quite different cases. The models in the literature such as unreacted shrinking core model, two stage model and homogeneous model can be considered as special cases of the above model which has been derived for leaching vanadium from steel slag with sodium carbonate and]or sodium bicarbonate solution reacting with two components in the slag simultaneously. The vanadium leaching reaction is inhibited by the solid product formed during the reaction. The power law equation can be used to represent the kinetic experimental data of leaching reaction. The model equations have been solved by orthogonal collocation and semi-implicit Runge-Kutta method. The parameters of the model have been estimated by the complex method. The calculated results based on this model is in good agreement with experimental data. The mathematical model of non-catalytic liquid-solid diffusion reactions discussed in this paper can be applied to quite different cases. The models in the literature such as unreacted shrinking core model, two stage model and homogeneous model can be considered as special cases of the above model which has been derived for leaching vanadium from steel slag with sodium carbonate and] or sodium bicarbonate solution reacting with two components in the slag simultaneously. The vanadium leaching reaction is inhibited by the solid product formed during the reaction. The model of have kinetic experimental data of leaching reaction. The model results have been solved by orthogonal collocation and semi-implicit Runge-Kutta method. The parameters of the model have been estimated by the complex method. The calculated results based on this model is in good agreement with experimental data.