A one-part curing system is generally applied to sealants, coatings and adhesives. Most of these sealants are moisture-curable. Cure speed prediction is very important when we design or handle these materials. Kinetic models are based on the moving boundary problems of mass transfer and moisture reaction. Pseudo-steady-state (PSS) models and unsteady-state (US) models are presented for a flat plate. Both models are expressed by three dimensionless parameters. Two boundary conditions and two conditions of m (the ratio of the equilibrium water concentration of the two phases on the boundary face), m = 1 and m not equal 1, were studied using the PSS and US. The US results were completely consistent with those by another numerical method. Not only the semi-infinite but also the finite distance to cure was studied. When the dimensionless curing time theta is greater than 1, PSS is in good agreement with US under all these conditions. As most of the sealants' theta values are greater than 1, the PSS model is accurate enough for the prediction. Experimental results supported these theories. The presented models apply not only to this one-part curing system, but also to similar phenomena such as the slow reaction of the oxidation of metals in air or the degradation of a polymer by oxygen and UV or gamma-radiation.