The resolution of civil liability claims is an expensive and uncertain process. Frequent parties to civil litigation face growing costs, but they might reduce the expense and uncertainty of litigation through new methods for using computers. Organizations that have experience in handling a large volume of civil litigation can use these methods to manage groups of cases and to organize single, complex cases. Four new methods for using computers — open claim analysis, closed claim analysis, decision analysis, and rule-based modeling — may reduce the direct costs of litigation and the indirect costs of uncertainty in evaluating civil claims. All four methods have been used to analyze and support decisions about litigation, but most have not been widely applied. This report describes the development, uses, and limitations of each method, so that insurance company claim departments, law firms, corporations, and other frequent parties to litigation can consider whether those methods might be of help.