Using a Plane-Wave Pseudo-Potential (PWPP) method, total energy and band structure calculations for M2TaN3, ε-TaN and MTa2N3 (M = a transition metal, TM) compounds have been performed in order to understand their structural stability and electronic properties. To do that, we first focus on ε-TaN compounds. The exchange correlation is treated using the Generalized Gradient Approximation (GGA). The Virtual Crystal Approximation (VCA) is then used to examine the structural stability when substituting Ti, Zr or Hf to a Ta atom either in a cell corner [c(M)(Ta2N3)] or inside the cell [in(M2)(TaN3)]. Actually, substitution of Ta by a Ti, Zr or Hf atom at a corner site does slightly change the corresponding lattice constant. Also we calculate ground-state quantities such as elastic constants, shear moduli, Young’s modulus and bulk modulus as well as Poisson’s ratio. The corresponding results for band structures and densities of states are shown as well. As far as we know our work is a pioneer attempt to determine elastic, mechanic and electronic properties for M2TaN3 and MTa2N3 (M = TM) compounds.