The U.S. Department of Energy Packaging Certification Program, Office of Environmental Management sponsors a training course on the application of the ASME Boiler and Pressure Vessel Code (ASME Code) to radioactive material transportation packaging, which has been conducted annually by Argonne National Laboratory since the early 2000s. The course was significantly expanded in 2013, from three to five days, to include the application of the ASME Code to storage casks for spent nuclear fuel and high-level radioactive waste. In 2015, the ASME Code course became part of the curriculum of the Graduate Certificate in Nuclear Packaging (GCNP) program at the University of Nevada, Reno. The purpose of this course is to provide guidance for the application of the ASME Code to Type B radioactive and fissile material transportation packagings and spent nuclear fuel storage casks, and to facilitate the design, fabrication, examination, and testing of packagings and casks. Both regulatory requirements in Title 10, Code of Federal Regulations, Parts 71 and 72, and the ASME Code requirements for transportation packagings and storage casks are addressed, with emphasis on Section III Division 3 of the ASME Code, Containments for Transportation and Storage of Spent Nuclear Fuel and High Level Radioactive Material and Waste; also discussed are Section II, Section III Division 1, Section V, Section VIII Division 1, and Sections IX and XI. Among the specific topics covered are the application of the Code requirements to structural materials, containments, loading and design, fabrication, welding, examination, testing requirements, quality assurance, aging management for long-term storage of spent fuel, transportation, and inspection and monitoring technologies. The ASME Code course is one of the three required courses for the GCNP program, the educational objectives of which are to provide the applied knowledge and skills required by mechanical, materials, and nuclear engineers to be successful as nuclear packaging designers, analysts, and users. Over 50 students have enrolled in the GCNP courses since 2015; the first GCNP Certificate was awarded in 2017. This paper will provide highlights of the ASME Code course, including lessons learned through feedback received from the course participants, and future directions.