Recently, SrHfO3 compound was proposed as a potential gate dielectric to fabricate metal–oxide–semiconductor field‐effect transistors (MOSFET) with equivalent oxide thickness (EOT) below 1 nm. Here we report the elasticity, electronic structure, and dielectric property of cubic SrHfO3 from first‐principle study based on the plane‐wave pseudopotential method within the local density approximation (LDA). The independent elastic constants of cubic SrHfO3 are derived from the derivative of total energy as a function of lattice strain. The elastic modulus is predicted from Voight‐Hill bounds. The Born effective charges, electronic dielectric tensors, long wavelength phonon frequencies, and LO–TO splitting of cubic SrHfO3 are computed by linear response with density functional perturbation theory (DFPT). The calculated lattice constant and bulk modulus of cubic SrHfO3 are in good agreement with the available experimental data and other theoretical results. Our results show cubic SrHfO3 is a ductile insulator with an indirect band gap of 3.74 eV (LDA value) and electric dielectric tensor of 4.43, Hf 5d states and O 2p states exhibit a strong hybridization, and cubic SrHfO3 can be mechanically stable. In addition, the phonon frequency of ‘soft mode' at zone‐center also agrees well with previous theoretical value. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)