The Grüneisen parameter of vitreous silica is of order -10 and strongly temperature dependent at 1.5 K, whereas in most crystalline solids it is of order +1 and temperature independent at similar temperatures. In this investigation the Grüneisen parameter has been determined by means of thermoelastic measurements. The temperature changes in rods of vitreous silica were monitored when mechanical strains were applied in the temperature range 1.5 - 17 K. Below ~5 K the Grüneisen parameter was found to depend on the average stain of the sample ; this dependence became more marked as the temperature was lowered, and at ~1.5 K the Grüneisen parameter became positive for large average stains. Irreversible effects were also observed indicating a broad distribution of relaxation times extending to times longer than 100s.