The transmission of soft x rays with photon energies from 1606 eV to 2106 eV was measured for tungsten using thin-film samples and a synchrotron source. This region includes the M IV and M V edges. The two tungsten films had thicknesses of 107.7Ϯ10 nm and 51.5Ϯ10 nm; the intensity of the transmitted x rays was measured with a silicon photodiode. The values for the mass absorption coefficient reported here were determined from the ratios of the transmission through the two samples, i.e., through a net 56.2Ϯ14 nm of tungsten, and some additional constant factors. The M V,IV edges have widths ͑10%-90% after background subtraction͒ of 33Ϯ5 eV and 28Ϯ5 eV, respectively, compared to zero width in all x-ray tables based on atomic form factors and to 41 eV and 44 eV within a real-space multiple-scattering theory. The measurements are relevant to microspectroscopy and microtomography of integrated circuit interconnects and may be applicable to accurate measurement of the mass absorption coefficients of similar dense elements.