Based on high throughput density functional theory calculations, we evaluated systematically the stability of 580 M2AX compounds. The thermodynamic, mechanical, and dynamical stability and the magnetic structure are calculated. We found 20 compounds fulfilling all three stability criteria, confirming Cr2AlC, Cr2GeC, Cr2GaC, Cr2GaN, and Mn2 GaC, which have been synthesized. The stability trends with respect to the M- and A-elements are discussed by analyzing the formation energies, indicating that Cr and Mn containing M2AX compounds are more stable than Fe, Co, or Ni containing compounds. Further insights on the stability are obtained by detailed analysis of the crystal orbital Hamilton population (COHP).