The adsorption of ethylene on a Pd(110) surface and the coadsorption with hydrogen is investigated using gradient corrected periodic density functional calculations, The surfaces have been modeled by 6 layers of Pd atoms for different unit cell sizes and geometries allowing us to study ethylene coverages from 0.125 to 0.5 monolayer (ML) and hydrogen from 0.125 to 1.0 ML. The adsorption energy and the geometry have been computed for different adsorption sites (on top of a Pd or bridging two Pd atoms) for different coverages. For bare Pd surfaces, at any coverage, the bridge site is always found to be more stable than any other site. This result is in contradiction with former interpretations of vibrational spectra. The validity of this result is then investigated further by computing the vibration frequencies associated with the different sites and by comparing the results to the experimental spectra. This comparison allows a reinterpretation of the experimental data and tends to confirm the validity of the bridge site found theoretically. The coadsorption of ethylene and hydrogen on the Pd(110) surface is then investigated with various structures and for different coverages of ethylene and hydrogen. The interaction between hydrogen and ethylene is found repulsive at short range and slightly attractive at long range. Hence, at medium or high coverage, the adsorption of hydrogen decreases the adsorption energy of the ethylene molecule on the surface. Furthermore, the bridge site is more destabilized than the top site with the hydrogen coverage increase: for a monolayer coverage of hydrogen, the two sites have roughly the same energy. An electronic interpretation of this phenomena is given. Finally, the comparison of the computed vibrational frequencies with the experimental results shows that, at low H coverage, the main site is still the bridge one, but that, at a higher coverage, the top site for ethylene becomes competitive.