Local anesthetics (LAs) are known to bind Na+ channels in the closed, open, and inactivated states and reach their binding sites via extracellular and intracellular access pathways. Despite intensive studies, no atomic-scale theory is available to explain the diverse experimental data on the LA actions. Here we attempt to contribute to this theory by simulating access and binding of LAs in the KcsA-based homology model of the closed Na+ channel. We used Monte Carlo minimizations to model the channel with representative local anesthetics N-(2,6-dimethylphenylcarbamoylmethyl)triethylammonium (QX-314), cocaine, and tetracaine. We found the nucleophilic central cavity to be a common binding region for the ammonium group of LAs, whose aromatic group can extend either along the pore axis (vertical binding mode) or to the III/IV domain interface (horizontal binding mode). The vertical mode was earlier predicted for the open channel, but only the horizontal mode is consistent with mutational data on the closed-channel block. To explore hypothetical access pathways of the permanently charged QX-314, we pulled the ligand via the selectivity filter, the closed activation gate, and the III/IV domain interface. Only the last pathway, which leads to the horizontal binding mode, did not impose steric obstacles. The LA ammonium group mobility within the central cavity was more restricted in the vertical mode than in the horizontal mode. Therefore, occupation of the selectivity-filter DEKA locus by a Na+ ion destabilizes the vertical mode, thus favoring the horizontal mode. LA binding in the closed channel requires the resident Na+ ion to leave the nucleophilic central cavity through the selectivity filter, whereas the LA egress should be coupled with reoccupation of the cavity by Na+. This hypothesis on the coupled movement of Na+ and LA in the closed channel explains seemingly contradictory data on how the outer-pore mutations as well as tetrodotoxin and micro-conotoxin binding affect the ingress and egress of LAs.