The phase velocities of acoustic shear‐wave motions in isotropic solids such as glasses can be influenced by residual or applied stresses that make the material acoustically birefringent (the acoustoelastic effect) in much the same way as residual or applied stresses make a transparent material optically birefringent (the photoelastic effect). When a uniaxial stress is applied to an isotropic solid, the acoustoelastic effect depends upon &mgr;, the shear modulus, and &ngr;3, one of the three third‐order elastic constants describing an isotropic solid. A method based on an analysis by Toupin and Bernstein is used to determine values of &ngr;3for four glasses: fused quartz and fused silica (two types of vitrous silica), Pyrex, and Bausch and Lomb T‐40 glass. The values of &ngr;3obtained for vitreous silica and Pyrex are compared with previously reported values. Although the paper includes results for Pyrex and T‐40 glass, the principal emphasis is on the results for vitreous silica and the significance of the findings regarding the acoustoelastic effect in vitreous silica for applications of this material in high‐frequency ultrasonic devices.