We report a calculation of the density of states (DOS) of quasi-particle excitations in the superconducting state of high T c cuprates using a model of the anisotropic gap that we have recently developed. This model is based on the van Hove scenario, that is on the assumption that the Fermi level lies close to singularities in the DOS. We compare this theoretical DOS to the results obtained in various tunneling experiments especially with break junction (S-I-S) and with vacuum scanning tunneling spectroscopy (N-I-S). The agreement is very good. We explain the structure observed in the gap; and with the van Hove singularity slightly below the Fermi level we reproduce the observed asymmetry in the conductance and the dip in the DOS that is also seen in photoemission.