Provided is a method of supporting a random access of MPEG data, the method including: obtaining at least one access unit including media data coded through processing including an encapsulation and a packetization; generating at least one media processing unit (MPU) by grouping at least one access unit; determining an initialization flag indicating whether the at least one access unit includes all of data required for initialization of a decoding process, in the at least one MPU; and inserting the initialization flag into a header of the at least one MPU.