The dynamic stability of non-linearly elastic composite plates subjected to periodic in-plane loading is investigated. Infinitely wide plates made of resin matrix composite are considered. The non-linearly elastic behavior of the resin matrix is modelled by the generalized Ramberg-Osgood representation. The effect of the matrix non-linearity on the overall response of the composite is predicted by the micromechanical method of cells. The dynamic stability analysis is performed by evaluating the largest Lyapunov exponent, the sign of which indicates whether the system is stable or not. It is shown that this approach forms a convenient tool for predicting parametric stability of non-linear composite structures.