The electronic structure, elastic constants and lattice dynamics of the B 2 type intermetallic compound LaAg are studied by means of density functional theory calculations with the generalized gradient approximation for exchange and correlation. The calculated equilibrium properties and elastic constants agree well with available experimental data. From the ratio between the bulk and shear moduli, LaAg is found to be ductile, which is unusual for B 2 type intermetallics. The computed band structure shows a dominant contribution from La 5d states near the Fermi level. The phonon dispersion relations, calculated using density functional perturbation theory, are in good agreement with available inelastic neutron scattering data. Under pressure, the phonon dispersions develop imaginary frequencies, starting at around 2.3GPa, in good accordance with the martensitic instability observed above 3.4GPa. By structural optimization the high pressure phase is identified as orthorhombic B 19. © 2012 IOP Publishing Ltd.