Neutron capture cross sections of four stable tungsten isotopes were measured as a function of energy by time of flight at the Oak Ridge Electron Linear Accelerator. The resolution achieved, ΔE/E of at full-width at half-maximum, has allowed the analysis of several hundred resonance peaks at energies a few kiloelectron volts above the neutron binding energy. Strength functions were fitted to the average cross sections up to ∼100 keV, and average cross sections were extended with less precision from 100 to 2000 keV. The capture cross section of natural tungsten was calculated from measurements for individual isotopes. Compound nucleus calculations have been made with deformed optical model parameters for comparison with experimental cross sections.