A steady-state performance model of multirow multipass cross-flow tubular heat exchangers is developed. The proposed matrix approach uses the concepts of local effectiveness, energy balance, and number of transfer units (NTU) applied to every pass/row in the cross-flow heat exchanger to predict thermal performance. The method can predict the total effectiveness of assemblies of heat exchangers. Several circuiting configurations, such as overall counter-cross-flow, overall parallel cross-flow, and fluids in parallel in one of the streams, were considered. Predictions of the steady heat transfer performance of selected multirow multipass cross-flow heat exchangers are obtained by applying the general matrix approach. The heat exchanger geometries selected for the comparative study represent common cross-flow heat exchanger configurations used in industry. For these heat exchangers the overall heat exchanger effectiveness values were computed for various capacity rate ratios and NTU values. The validity of the matrix approach was then verified by comparing the resulting predictions with those obtained using the P-NTU approach and the Domingos method for the selected complex cross-flow heat exchanger configurations.