The shape of electro-vibrational bands in near-edge x-ray absorption fine structure (NEXAFS) spectra is often made up by a few strong lines near a phononless resonance. In addition-as predicted here-there can be extended tails due to the large density of vibrational states in the short-wavelength region of the x-ray spectrum where the spacings between vibrational levels are smaller than the lifetime broadening. We propose a continuum approach for simulating vibronic bands in x-ray absorption spectra for systems with a high density of states. This approach is found to provide an accurate description of the spectral shape of the multi-mode vibrational bands in the NEXAFS spectra of polyenes having even a relatively small number of vibrational modes. Ab initio simulations using the discrete linear coupling model confirm the common trends obtained by the continuum approach.