The effects of mixed-valence Mn substitution at the Cu site on the superconducting and elastic properties of La1.85-1.5xSr0.15+1.5xCu1-xMnx O4 (x = 0, 0.02 and 0.04) were studied. The samples were characterized by X-ray diffraction (XRD) method, temperature-dependent resistance measurements, scanning electron microscopy (SEM) and sound velocity measurements at room temperature. An elastic softening and a decrease in the critical temperature Tc was observed as Mn was substituted for Cu. The Debye temperature θD for x = 0 and 0.02 void free samples were calculated to be 459 K and 430 K, respectively. Internal lattice strain which is related to lattice parameter ratio a/c did not correlate with Tc . The electron-phonon coupling estimated using the conventional Bardeen-Cooper-Schrieffer (BCS) theory was λ = 0.367 (x = 0) and 0.368 (x = 0.02). The electron-phonon coupling in two-dimensional van Hove scenario was calculated to be λvH = 0.0148 (x = 0) and 0.0149 (x = 0.02). These results were compared with other cuprates and related superconductors. The comparison showed that other than electron-phonon coupling, the elastic moduli might play an important role in the mechanism of superconductivity in these materials.