Rare earths are listed as crisis minerals，key raw materials or strategic minerals by countries around the world.Taking the trade networks of main rare earth products as the research object，the research gets trade data of 7 kinds of rare earth products from 54 major countries（or regions） during the period of 2009—2020，and the evolution of 7 rare earth products trade networks was compared by social network analysis，and the basis of trade network formation mechanism was explained by using the Exponential Random Graph Model（ERGM） analysis method.The conclusions are as follows：（1）Trade network links of some rare earth products，such as rare earth mineral substances，compounds of rare-earth metals，Ferro-cerium and permanent magnet，are getting tight.While the overall structures of all the networks are still relatively loose.Trade networks of all rare earth products have a high community structure and connectivity，showing a small world property but gradually weakening.（2）In the trade networks of 7 rare earth products，it can be easily found that huge trade volumes are controlled by a few countries，with an obvious center-periphery phenomenon.Rich Club Phenomenon is significant in trade networks of rare earth metals，rare-earth compounds，cerium compounds，Ferro-cerium and Ferro-alloys.（3）Countries’ performance in Degree Centrality remain stable.Germany and China are both core countries，but Germany’s advantage is weakening while China strengthening.（4）Influences of mutualism，multi-connectivity，transitive closure，convergence and expansionary structural effects on trade network evolution of 7 rare earth products are significantly heterogeneous.The research results provide policy enlightenment for China to strengthen the strategic research and judgment of the new pattern and new situation of global rare earth product trade and alleviate economic and trade frictions.