Abstract:  In electromagnetism，we often deal with the problem of catastrophe surface of electromagnetic medi-um，which means that the dielectric constant or permeability changes suddenly at the interface． Generally，when dealing with such problems，we will use boundary conditions to deduce the relationship between physical quantities on both sides of the catastrophe surface． On this basis，this paper will repair the existing electromagnetic medium theory，so that the catastrophe surface of electromagnetic medium has a clearer mathematical model，and can accu-rately describe the points on the boundary． This paper is mainly for freshmen who are studying electromagnetism in grade one or grade two． Relevant examples will also be provided at the end of the paper，hoping to help and inspire them to deal with problems in their usual classroom or homework．

Key words:  electromagnetic medium, second kind of Gaussian closed surface, second kind of Gaussian closed curve, boundary vector