We have performed accurate ab‐initio total energy calculations using the full‐potential linearized augmented plane wave (FP‐LAPW) method with the generalized gradient approximation (GGA) for the exchange‐correlation potential to investigate the elastic, electronic and cohesive properties of hexagonal and cubic polymorphs of WC and WN. The optimized lattice parameters, independent elastic constants (Cij), bulk moduli (B), shear moduli (G), as well as band structure, density of states, electron density distribution and cohesive energies are obtained and analyzed in comparison with the available theoretical and experimental data. In addition, for the first time, the numerical estimates are made for some elastic parameters of the polycrystalline WC and WN ceramics (in the framework of the Voigt–Reuss–Hill approximation), namely bulk and shear moduli, compressibility (β), Young's moduli (Y), Poisson's ratio (ν) and Lamé's coefficients (μ, λ). (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)