We have investigated various silica zeolites using density functional theory with periodic supercells, plane waves, and pseudopotentials. These zeolitic phases include silica sodalite, chabazite, mordenite, silica LTA, and silicalite. Atom-level geometries, elastic properties, and cohesive energies are presented. Although the zeolites exhibit a wide range of Si-O-Si angles and densities, the cohesive energies remain nearly constant. The elastic properties vary significantly from one phase to another, and in some cases, large elastic anisotropies are observed.