The influence of molecular vibrations on the low-lying electronic levels of short oligomers of poly(para-phenylene) is studied. Within an interacting molecular orbital basis, the complete electron-phonon Hamiltonian is diagonalized numerically. Energy shifts and equilibrium phonon displacements are calculated for the totally symmetric vibrational modes. For the 1 (1)A(g)(+)-1 B-1(u)- transition, Huang-Rhys and Franck-Condon factors, as well as the change of equilibrium geometry, are computed. The importance of vibrations with a frequency of about 0.2 eV is confirmed. The intrinsic Stokes shift is found to be zero, in agreement with experimental data.