In the present study, the structural, electronic, optical, and mechanical properties of the Ruddlesden-Popper type oxide compounds are investigated by means of density functional theory. In our calculation, spin polarized electron band structures and density of the state were identified by adding to the spin contribution of the Mn-atom. For A3Mn2O7 compounds, the real and imaginary parts of the dielectric function and other optical properties, such as energy loss function, effective number of valence electrons, and effective optical dielectric constant, were calculated accordingly. In addition, the bulk modules, shear modules, Young's modulus and Poisson ratios, anisotropy factors, sound velocities, and Debye temperatures for these compounds were calculated too.