A theory is presented describing mode conversion and tunneling in a warm, collisionless, toroidal plasma near the first ion‐cyclotron harmonic frequency when the waves are propagating perpendicular to the static magnetic field. The coupling region may be characterized by a fourth‐order differential equation with one turning point. Employing the method of Laplace integrals and the method of matched asymptotic expansions, transmission, reflection, and conversion coefficients are calculated assuming a fast wave is incident from either side of the coupling region. For a fast wave incident from the low magnetic field side, transmission, reflection, and conversion occur, while for a fast wave incident from the high magnetic field side, only transmission and conversion occur with no reflection, independent of the thickness of the tunneling layer, which implies complete conversion of the fast wave to the slow wave as the tunneling layer becomes thick. The problem of cavity resonance is discussed.