The electron-phonon coupling constant of the copper oxide-based high temperature superconductors in the van Hove scenario was calculated using three known models and by employing various acoustic data. Three expressions for the transition temperature from the models were used to calculate the constants. All three models assumed a logarithmic singularity in the density of states near the Fermi surface. The calculated electron-phonon coupling constant ranged from 0.06 to 0.28. The constants increased with the transition temperature indicating a strong correlation between electron-phonon coupling and superconductivity in these materials. These values were smaller than the values estimated for the conventional three-dimensional BCS theory. The results were compared with previous reports on direct measurements of electron-phonon coupling constants in the copper oxide based superconductors.