This paper reports numerical simulations of the structure of the reaction zone and adjoining flow of a steady-state two-dimensional detonation wave in an unconfined cylindrical charge in order to study the shock shape, sonic locus, streamlines, and characteristic lines. The reactive fluid dynamic equations are solved by the flux-corrected transport technique and making no a priori assumptions about the flow structure. The polytropic reactive fluid with the simple heat-release law is used as a model. The results of the simulations, when compared to the theoretical analysis, elucidate some fundamental features of the reaction-zone structure. In particular, the calculations show that two different forms of the sonic loci are possible, depending on the charge diameter. Near the charge edge, the sonic locus is always tangential to the upstream limiting characteristic of the rarefaction fan. In the vicinity of the sonic surface, the streamlines have inflection points, and unresolved singularities at the characteristic lines are expected. The sonic surface limits the part of the reaction zone which has any influence on the detonation front.