This multicenter, prospective, randomized clinical trial will compare the radiologic procedure of TIPS with the surgical procedure of DSRS for variceal bleeding. The health relatedness is to define the relative merits of these two treatments with respect to morbidity, mortality and management cost. The hypothesis to be tested is that TIPS will have a significantly higher rebleeding rate and incidence of encephalopathy than DSRS. Uncontrolled studies show a variceal rebleeding rate of 20% after TIPS, compared to 5% after DSRS, and an encephalopathy incidence of 30% after TIPS, compared to 14% after DSRS. In this study, Child's Class A and B patients with variceal bleeding which cannot be managed by endoscopy will be randomized to TIPS or DSRS. It is estimated that 140 patients need to be entered and that this population can be accrued over the initial three years of this study. A minimum follow up of two years is planned to the primary end points of variceal rebleeding and hepatic encephalopathy. The secondary end points will be death, ascites, need for liver transplant, shunt thrombosis or stenosis, liver function, quality of life and cost. The coordinating center will be responsible for data verification, data management and statistical analysis. Significant differences in primary end points are expected in 12-24 months: some of the secondary end points, death and need for transplant, may require longer follow up. The four centers participating in this trial have experience with the type of patients under study, the procedures to be tested, and conduct of controlled trials. This should be the definitive trial comparing TIPS to surgical decompression of varices.