Preservation of similitude criteria in current mathematical models used for transient analysis of thermal-hydraulic systems is discussed. Input models for the RELAP5 computer code were developed at the Idaho National Engineering Laboratory for two simple hypothetical natural circulation systems consisting of a closed loop containing energy generation, energy removal, and flow resistance. The two models differed significantly in geometric scale size. A reference model had components and operating conditions in a range similar to those found in typical nuclear steam supply systems; a scaled model, geometrically much smaller than the reference model, had components that were sized from the reference model using similarity criteria presented in the literature. Steady-state and transient single- and two-phase natural circulation calculations were conducted using both models to determine if the model-to-model relationships in time, pressure drop, and velocity scales were in accordance with the similitude criteria. Results indicate that, while the code predicts the expected fundamental effects of geometric scale, there are noteworthy differences in the details of calculations.