The general approach to Alfvén-wave current drive and induced plasma rotation in tokamaks with strongly elongated transverse cross-sections is considered. Model approximations are used to describe the circulating- and trapped-particle dynamics in all particle-trapping regions. This approach gives an accuracy of some percent. New terms, connected with the wave dissipation on trapped particles in the second and third trapped-particle regions for elongated tokamaks, are taken into account. The plasma rotation and longitudinal current, depending on the absorbed power of kinetic Alfvén waves, are discussed.