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Structural, elastic, electronic and magnetic properties of the Nickel-based magnetic shape memory alloys (MSMA) Ni2MnSb, Ni2MnSn and Ni2MnSb0.5Sn0.5, are investigated using the full-potential linearized plane wave plus local orbital method (FP-LAPW+lo). With Perdew-Burke-Ernzerhof (PBE) exchange-correlation, generalized gradient approximation (GGA) is used to describe the electronic exchange correlations energy. Equilibrium lattice constant, bulk modulus, and its pressure derivative are calculated and compared with available data. Using the total energy versus strain in the framework of the FP-LAPW+lo approach, we compute the elastic constants of the studied compounds in their austenite structure. Good agreement is found with other calculations both for Ni2MnSb and Ni2MnSn. Magnetic moments agree well with available results.