This study is concerned with the modeling of plate buckling induced by a chemical reaction and is inspired by the observation that buckling may be a mechanism of stress relaxation in Si-based anodes in Li-ion batteries. A chemical reaction is localized at a sharp interface and accompanied by transformation strains, which produce internal stresses. If external supports restrict the deformation of the plate, buckling may occur. At the same time, mechanical stresses affect the kinetics of the reaction. The chemical affinity tensor concept allows us to couple the stresses with the chemical reaction rate. We formulate a coupled problem for a plate with two reaction fronts and find the critical thickness of the transformed material and the time before buckling. The influence of the material and geometrical parameters on the buckling occurrence and the time until buckling is studied.