The influence of the electromagnetic properties of the substrate upon the size effect in hard superconductors is theoretically studied. Within the frame of the critical state model we calculate the distribution of the magnetic induction and the electric field inside a superconducting plate subject to unilateral electromagnetic excitation. This calculation allows to obtain the dependences of surface impedance and absorptivity on the amplitude of the external signal. We find that the manifestation of the size effect in the ac response of the superconducting plate depends strongly on the value of the dielectric constant of the substrate. ©1996 American Institute of Physics.