First-principles self-consistent pseudopotential plane wave calculations based on density functional theory were performed in order to study magnetic moments, density of states and half-metallicity of L2(1) type full Heusler alloys with formula Co2MnX (X = Si, Ge, Al, Ga). Half-metallicity in terms of total spin-moments was discussed since perfect half-metals show Slater-Pauling (SP) behavior. The effects of the atomic number on the lattice constants, the bulk moduli and the Curie temperatures were shown. The magnetic moments were calculated, while slight deviations of about 0.06-0.16 mu(B) were found for Co2MnAl and Co2MnGa, the Co2MnSi and Co2MnGe have been found to be half metals. Mechanical stability of these compounds has been analyzed in terms of their elastic constants. The size of the gap in the minority states and the position of E-F inside the gap was also discussed as it is an important factor for the application of half-metallic ferromagnetic alloys. Finally, phonon dispersion curves and the density of states were calculated by employing the density-functional perturbation theory and discussed. (C) 2013 Elsevier B.V. All rights reserved.