We report density functional theory calculations on the crystal structure, elastic, lattice dynamics and electronic properties of iso-structural layered monoclinic alkali azides, LiN3 and NaN3. The effect of van der Waals interactions on the ground-state structural properties is studied by using various dispersion corrected density functionals. Based on the equilibrium crystal structure, the elastic constants, phonon dispersion and phonon density of states of the compounds are calculated. The accurate energy band gaps are obtained by using the recently developed Tran Blaha-modified Becke Johnson (TB-mBJ) functional and found that both the azides are direct band gap insulators. (C) 2013 Elsevier B.V. All rights reserved.