The electric field-induced translocation of cylindrical particles through nanopores with circular cross sections is studied theoretically. The coupled Nernst-Planck equations (multi-ion model, MIM) for the concentration fields of the ions in solution and the Stokes equation for the flow field are solved simultaneously. The predictions of the multi-ion model are compared with the predictions of two simplified models based on the Poisson-Boltzmann equation (PBM) and the Smoluchowski's slip velocity (SVM). The concentration field, the ionic current though the pore, and the particle's velocity are computed as functions of the particle's size, location, and electric charge; the pore's size and electric charge; the electric field intensity; and the bulk solution's concentration. In qualitative agreement with experimental data, the MIM predicts that, depending on the bulk solution's concentration, the translocating particle may either block or enhance the ionic current. When the thickness of the electric double layer is relatively large, the PBM and SVM predictions do not agree with the MIM predictions. The limitations of the PBM and SVM are delineated. The theoretical predictions are compared with and used to explain experimental data pertaining to the translocation of DNA molecules through nanopores.