Antenna coupling to the shear Alfven wave by both direct excitation and fast-wave resonant-mode conversion is modelled analytically for a plasma with a one-dimensional linear density gradient. We demonstrate the existence of a shear Alfven mode excited directly by the antenna. For localized antennae, this mode propagates as a guided beam along the steady magnetic field lines intersecting the antenna. Shear Alfven wave excitation by resonant-mode conversion of a fast wave near the Alfven resonance layer is also demonstrated and we prove that energy is conserved in this process. We compare the efficiency of these two mechanisms of shear Alfven wave excitation and present a simple analytical formula giving the ratio of the coupled powers. Finally, we discuss the interpretation of some experimental results.