The structural, elastic, phonon and electronic properties of a MnPd alloy have been investigated using the firstprinciples calculation. The calculated lattice constants and electronic structure agree well with the experimental results. The microscopic mechanism of the diffusionless martensitic transition from the paramagnetic B2 (PM-B2) phase to the antiferromagnetic L1 0 (AFM-L1 0) phase through the intermediate paramagnetic L1 0 (PM-L1 0) phase has been explored theoretically. The obtained negative shear modulus C ′ = (C 11 − C 12)/2 of the PM-B2 phase is closely related to the instability of the cubic B2 phase with respect to the tetragonal distortions. The calculated phonon dispersions for the PM-L1 0 and AFM-L1 0 phases indicate that they are dynamically stable. However, the AFM-L1 0 phase is energetically most favorable according to the calculated total energy order, so the PM-L1 0 →AFM-L1 0 transition is caused by the magnetism rather than the electron-phonon interaction. Additionally, the AFM-L1 0 state is stabilized through the formation of a pseudo gap located at the Fermi level. The calculated results show that the CuAu-I type structure in the collinear antiferromagnetic state is dynamically and mechanically stable, thus is the low temperature phase.