The mechanism of DNA elongation in nanochannels was explored by Monte Carlo simulations as a function of the channel dimension D, DNA length, and stiffness. Simulations were based on the bead-spring model, representing double-stranded DNA chains of moderate length at a high salt concentration. As a rule, the channel-induced elongation profiles of R-II vs D from the simulations were in qualitative agreement with those: from microfluidic measurements of DNA. The longitudinal chain elongation in narrow channels was found to be correctly predicted by the Odijk relation for the deflection regime. The scaling relation of R-II vs D-1, based on the statistics of ideal-chain blobs, was used to explain the simulation data at the intermediate channel widths. Contrary to the blob-theory presumption, the nonlinear dependence of DNA elongation R-II on the: chain length N was observed in simulations at moderate confinement. It was suggested that discrepancies found between the simulations and the blob theory arose from the formation of various DNA hairpin structures within channels.