Many atmospheres (cool stars, brown dwarfs, giant planets, extrasolar planets) are predominately composed of molecular hydrogen and helium. H$_2{}^{16}$O is one of the best measured molecules in extrasolar planetary atmospheres to date and a major compound in the atmospheres of brown-dwarfs and oxygen-rich cool stars, yet the scope of experimental and theoretical studies on the pressure broadening of water vapour lines by collision with hydrogen and helium remains limited. Theoretical H$_2$- and He-broadening parameters of water vapour lines (rotational quantum number $J$ up to 50) are obtained for temperatures in the range 300 - 2000 K. Two approaches for calculation of line widths were used: (i) the averaged energy difference method and (ii) the empirical expression for $J$\p $J$\pp-dependence. Voigt profiles based on these widths and the BT2 line list are used to generate high resolution ($Δ \tilde{\nu}$ = 0.01 \cm) pressure broadened cross sections for a fixed range of temperatures and pressures between 300 - 2000 K and 0.001 - 10 bar. An interpolation procedure which can be used to determine cross sections at intermediate temperature and pressure is described. Pressure broadening parameters and cross sections are presented in new ExoMol format. ; Comment: 40 pages, 5 Figures, 6 Tables JQSRT, in press