The effect of mode conversion on antenna-plasma coupling in the ICRH rangeis studied. A collisionless, weakly inhomogeneous plasma in the `slab'approximation, in which mode conversion is described by the tunnellingequation with first harmonic majority (ω = 2ΩcM)and fundamental minority (ω = Ωcm) ion cyclotronabsorption, is considered. Green's function, connecting the electric field on an ICRH antennawith the current flowing in the same antenna, has been evaluated,essentially in closed form, and has beenemployed to evaluate the antenna radiation resistance. Numerical results have been obtained, for the parameters of the IGNITORmachine and a deuterium-hydrogen plasma; in the coldplasma limit, in which mode conversion effects are disregarded, ourresults are in agreement with those of an established code. Mode conversion effects produce a decrease of the radiationresistance for the monopole antenna configuration, and much weakereffects on the dipole configuration. This is related to the behaviour of the real part of the Green's function, which tends to vanish rapidly for toroidalwavenumbers approaching zero as a result of reflection from themode conversion layer.