The competition between drying and reactions in a liquid coating containing precursors to a random network polymer can give rise to a variety of drying phenomena. Solidification, or gelation, of the polymer may occur before, after, or during the removal of solvents from the coating. Rates of drying and reaction are probed by solving the equations of mass transfer by diffusion along with chemical reaction in one dimension. Solutions to this system of equations are obtained by Galerkin's method with finite-element basis functions and entail large-scale computation. Skinning, or solidification at the surface of the coating while the bulk is still liquid, occurs in thick coatings when the diffusional resistance to drying is significant, that is, at high mass-transfer coefficients. Homogeneous solidification occurs in thin coatings at low mass-transfer coefficients. Drying regime maps represent these solidification phenomena as regions in parameter space.