We have examined one of the key predictions of the magnetospheric infall model for classical T Tauri stars (CTTS), namely, the formation of a shock on the stellar surface. We find that accretion column emission can successfully reproduce the main observational properties of the excess continuum that veils the absorption features in CTTS. This success adds further support to the magnetospheric infall model for disk accretion. We have calculated the structure and the spectral energy distribution of the emergent continuum emission from a shock at the base of the magnetospheric accretion column. We find that the spectral shape of the excess can be understood as optically thick emission from the heated photosphere below the shock, appearing mostly on the Paschen and Brackett continua, and optically thin emission from the preshock and attenuated postshock regions, dominating at wavelengths shorter than the Balmer threshold. The accretion luminosity and rate depend on two parameters: the energy flux of the accretion flow, Script F, and the surface coverage of the column, f, with typical values log Script F~10.5-11.5, of the order or up to a factor of 10 higher than the intrinsic stellar flux, and f ~ 0.1%-1% of the surface area. The so-called continuum stars have accretion columns with similar energy fluxes than the less veiled, typical CTTS but with much larger surface emitting areas of f ≥ 10%. At near-infrared wavelengths, the predicted veiling from the accretion column for typical CTTS parameters is nearly constant and ≤0.1. Only for the "continuum stars" are significant amounts of near-infrared veiling from the accretion column expected. For accretion columns with low values of Script F, the Paschen continuum emission has spectral features, rendering the usual deveiling procedures uncertain. Magnetospheric flow Balmer emission may also contribute to the excess for stars with low-Script F columns. Finally, accretion column emission can successfully reproduce the observed correlation between the excess luminosity at the U band and the accretion luminosity. This correlation does not depend on the characteristics (mass, spectral type) of the underlying star, at least in the range M3-K5.