A method of seeking a vacant memory area uses area management tables having 1 MB and 4 kB unit area sizes for controlling the vacancy/occupancy status of each unit area of a file allocation space in a disk memory, and a free area seek program which seeks a vacant area of a requested size by selectively using the tables depending on the requested size. The program first seeks a vacant area based on the table of larger unit area size to thereby determine the major part the area required and then seeks a vacant area based on the table of smaller unit area size for determining the rest of the area required.