Rare metals (RMs) are becoming increasingly important in high-tech industries associated with the Fourth Industrial Revolution, such as the electric vehicle (EV) and 3D printer industries. As the growth of these industries accelerates in the near future, manufacturers will also face greater RM supply risks. For this reason, many countries are putting considerable effort into securing the RM supply. For example, countries including Japan, Korea, and the USA have adopted two major policies: the stockpile system and Extended Producer Responsibility (EPR). Therefore, it is necessary for the manufacturers with RMs to establish a suitable supply chain plan that reflects this situation. In this study, the RM classification matrix is created based on the stockpile and recycling level in Korea. Accordingly, three different types of supply chain are designed in order to develop the closed-loop supply chain (CLSC) planning model of RM, and the CLSC planning models of RM are validated through experimental analysis. The results show that the stockpiling and the EPR recycling obligation increase the amount of recycled flow and reduce the total cost of the part manufacturing, which means that these two factors are significant for obtaining sustainability of the RMs' CLSC. In addition, the government needs to set an appropriate sharing cost for promoting the manufacturer's recycling. Also, from the manufacturer's perspective, it is better to increase the return rate by making a contract with the collectors to guarantee the collection of used products.