To transfer a file comprising block data at high speed between sequential access type auxiliary memories, a file transmission program inquires of an operating system about the physical storage positions of the block data, determines a reading order to reduce the read access time on the basis of the results of inquiry, and issues read requests sequentially to the operating system according to the reading order. The file transmission program requests the operating system to transmit the read block data. The block data together with respective logical identification data, for example, logical block numbers, are transmitted to a receiving end which may be another computing system. The operating system at the receiving end is requested to secure the number of physical data blocks required to store the block data. The write order of the block data to the physical data blocks is then determined to reduce the access time and the block data are respectively stored in the secured physical data blocks according to the write order. Sequentially, a pair of the logical identifiers of each block data actually written to the data area and physical identification data of the data blocks are stored in the data area.