In the immediate aftermath of last October's stock market crash, some 650 American companies announced share repurchase programmes. Even though in most cases the volume of purchases under these programmes may have been nugatory, it seems likely that the announcements themselves exerted a steadying influence on share prices. In the United Kingdom, by contrast, there was no significant increase in share repurchase proposals by companies. This paper examines the rationale for share repurchases and the legal and taxation framework which governs them in the United Kingdom. Comparisons are drawn with the regimes in the United States and elsewhere. The paper concludes by suggesting that company managements and shareholders in the United Kingdom should be more prepared than hitherto to give consideration to share repurchase as a possible component of companies' financial strategy.