Two technologically important tungstate crystals - CdWO4 and ZnWO4 - are studied theoretically using the plane wave based first-principles calculations. The optimized crystal structures were used to calculate the structural, electronic and elastic properties of both materials under varying hydrostatic pressure. It was shown that the band gaps, which are direct at ambient pressure, turn into indirect ones in both compounds in the pressure range from 5 to 10 GPa, whereas the values of the band gaps themselves depend only slightly on the applied pressure. Differences in compressibility along the crystallographic axes and the W-O, Cd-O, Zn-O chemical bonds were revealed and quantified by calculating the pressure coefficients for all these characteristic distances. The first estimations of the complete elastic tensor constants for both materials are reported. (C) 2012 Elsevier B.V. All rights reserved.