Mathematical models are presented for describing and analyzing indicator dilution curves recorded in patients with intracardiac and great vessel shunts. The models treat individual segments of the circulation as linear system blocks, each having, at its output, a characteristic time response to a rapid injection of indicator at its input. These blocks are combined in feedback and feed-forward configurations to simulate left-to-right, right-to-left, and bidirectional shunts. A shunt analysis algorithm, using discrete analogs of the linear system models, was implemented in a computer program and used to analyze thermodilution curves recorded in patients with congenital heart defects. Results are presented comparing shunt fractions obtained from thermodilution curve analyses with oximetrically determined values in 20 patients. Comparing left-to-right shunts measured by the two methods, the mean systematic difference was 0.7% of pulmonary flow and the standard deviation was 7.6% of pulmonary flow. Statistical validation of the bidirectional shunt method will require acquisition and analysis of more data; however, reasonable shunt fractions were computed in five cases studied and good agreement with oximetric determinations was obtained in two cases where complete oximetric data were available.