Magnetism, electronic structure, elastic and thermal properties of Mn2YAl (with Y = Cr, V) have been investigated. The optimized lattice parameters, bulk modulus, and cohesive energy have been obtained. These alloys have the ferrimagnetic state as the most stable magnetic configuration, since the calculations showed a strong Mn-V antiferromagnetic coupling leading to the ferromagnetism of the Mn sublattices. A small and itinerant magnetic moment of Mn at the A site is found, which is antiparallel to the moment of Y at the B position in Mn2YAl (with Y = Cr, V) compounds. The calculated total spin moments are integral values and increase from − 2 μB/f.u. for Mn2VAl to – 1 μB/f.u. for Mn2CrAl with increasing the number of valence electrons. Band structure and total and partial density of states could be calculated via applying the modified Becke Johnson approximation (mBJ). Based on these results, Mn2YAl (with Y = Cr, V) are half-metallic ferrimagnets with the energy gap lies in the majority spin direction and a high-spin polarization (100%). The main difference between these two compounds is that the band gap is increased by 48% (0.210 eV for Mn2CrAl and 0.401 eV Mn2VAl). Elastic anisotropies, brittleness, and thermodynamic properties are determined for the Mn2YAl (with Y = Cr, V). The slight difference in the spatial distributions of Young’s moduli of Mn2YAl (with Y = Cr, V) reflects the small differences for the elastic anisotropies of the alloys under consideration. The mechanical stability of Mn2YAl (with Y = Cr, V) alloys are studied based on the elastic constants. The thermal properties are studied and investigated using the quasi-harmonic model, in addition, the temperature effect on heat capacities at constant pressure and volume, entropy, and thermal expansion are analyzed and discussed.