In this work, density functional theory calculations on the structural, mechanical, and lattice dynamical properties of AgB2 and AuB2 compounds in AlB2, OsB2, and ReB2 structures are reported. Generalized gradient approximation has been used for modeling exchange-correlation effects. The detailed information is given for the energetically most stable structure for AgB2 and AuB2 compounds. Specifically, the lattice parameters, bulk modulus, cohesive energies, elastic constants, shear modulus, Young's modulus, Poison's ratio, Debye temperature, sound velocities, and anisotropic factors are studied. The elastic properties are also studied under pressure. The phonon dispersion curves and corresponding phonon density of states are calculated and discussed. Our structural and some other results are in agreement with the available experimental and theoretical data. (C) 2011 Elsevier B.V. All rights reserved.