We investigate theoretically the aspect-ratio dependence of Alfvén-wave current drive (AWCD) in ‘simulated’ tokamaks, in the range 1.1[les ]R/a[les ]10 (where R and a are the major and minor radii, respectively). The study is carried out within the framework of resistive MHD, and is based on the consistent solution of the full-wave equation (E∥≠0); both shear and simulated toroidicity effects are taken into account. The AWCD includes components due to (wave) momentum transfer, helicity injection and plasma flow. The aspect-ratio-dependent features investigated include the radial profiles as well as the integrated power absorption, current drive and efficiency; the effects of antenna parameters (wavenumbers and frequency) are also explored. The numerical code developed and used for these computations has been benchmarked with the aid of analytical solutions obtained for the antenna–metallic-wall system in vacuum, as well as by the smooth transition from the vacuum case to the actual plasma case. Results of extensive calculations for the so-called Alfvén-continuum frequency range are presented and discussed.