Abstract: Researches on mathematical models of river flow and sediment transport by Changjiang/Yangtze River Scientific Research Institute (CRSRI) can be traced back to the 1950s, with a series of computer software of “ Heliu ” (or “ River ” ) been developed over the last 6 decades of development and application. This paper makes a review on key mathematical models at CRSRI, which comprises the reservoir sedimentation model, river 1-D, 2-D and 3-D models, and other mathematical models and application practices, inclusive of estimating models, special models and imported models. Core technologies of numerical simulation of river flow and sediment transport are also presented. To establish a system for the models, improve the existing models, expand the modeling disciplines and applications, and make breakthroughs in modeling techniques are major tasks for the model development. The paper can be regarded as a guideline for the development of the models in CRSRI.

Key words: mathematical model of river flow and sediment transport ,  , computer software of “Heliu ” , hydraulics and river dynamics