data write/read control apparatus, provided between a numerical control device and a cassette memory for writing data into the cassette memory and for reading data out of the cassette memory, as well as a method of controlling the data write/read operations. In a data write operation, a file is divided into a plurality of blocks, each comprising a predetermined number of bytes, one file constituting one input unit of data written into the cassette memory from the numerical control device. A control byte is added to the head part of each block and, when the amount of remaining storage space in the cassette memory is equivalent to one block of data, a code, indicating a shift to a subsequent cassette memory, is written in the control byte of the last block stored in the cassette memory. An external indication is given instructing when to exchange the cassette memory for the subsequent cassette. In a data read operation, the code indicating cassette exchange is sensed, whereupon an external indication is given instructing exchange of the cassette.