Seventy years ago, in 1955, the world’s first experimental ice basin was built at the Arctic and Antarctic Research Institute in Leningrad, enabling model-based analysis of ice resistance to ships sailing in ice-infested waters. The ice basin construction was preceded by a twenty-year period of attempts to adapt model experiments to ice conditions. These studies were undertaken by V.I. Neganov, L.M. Nogid and V.S. Nazarov. It became clear that in order to design and build an ice basin it was necessary to develop a physical ice model, as well as a theory of modeling and extrapolation of model scale data to full size. The theory of modeling and the necessary similarity criteria were developed by Professor L.M. Nogid and Academician Yu.A. Shimansky. Now these criteria are used in all the ice basins of the world. The paper considers the difference in approaches to modeling suggested by the above-mentioned researchers. The development of modeling criteria and test data scaling methods was not a short story because the choice of one or another version of theory was substantially dependent on the physical model of ice applied in the ice basin. Initially, L.M. Nogid and AАRI administration thought of using an artificial ice cover made of paraffin mixed with animal oil. The final choice of modeling criteria became possible only after V.V. Lavrov had developed procedures for preparing simulated ice followed by exploration of its properties, and the feasibility of icebreakers’ model tests in such ice had been proved in the Vedeneev VNIIG water tank. Based on archival documents and publications that are difficult to access due to security classification, the paper examines the history of similarity criteria development for the ship motion in ice in model and full scale. The elaboration of these criteria enabled AАRI to develop and commission the first ice basin in the world.