A semi-kinetic model of the ions in the solar corona is presented, which includes the effects of wave-particle interactions and Coulomb collisions. At the coronal base a spectrum of Alfv¿n waves is assumed. The spatiotemporal evolution of the spectrum in a 2-D computational domain is determined, taking the absorption of the waves by the particles into account. Integration over the velocity components perpendicular to the magnetic field yields reduced velocity distribution functions, for which a Vlasov equation is derived and solved numerically. The results obtained for a model of the heating process in a coronal funnel and in the lower corona are presented. The calculated velocity distribution functions show distinct kinetic effects and reflect key properties of the corona as observed by SOHO. ¿ 2001 American Geophysical Union