A Monte-Carlo investigation of ion cyclotron resonance heating of tokamak plasmas is undertaken to study the effect of finite banana width orbits on the efficiency of the heating process. For minority heating schemes with peaked power deposition profiles, there is a significant reduction in absorbed and transferred power in the centre of the discharge compared with zero orbit width calculations. The broader power transfer profiles give rise to a large reduction of tail energy in the centre while the total fast ion energy content and the total thermonuclear yield are less affected. The reduction of the power absorption in the centre for fixed wave field profiles arise because of the broadening of the orbits and. the enhanced diffusion and drift of the heated ions. The importance of these effects is assessed.