A main memory shared by plural processing units in a parallel computer system is composed of plural partial main memories. A directory for each data line of the main memory is generated after the data line has been cached in one of the processing units. The directory is held in one of the partial main memories in place of the data line. The directory indicates a processing unit which has cached the data line. A status bit C provided for the data line is set. If a subsequent read request is given to the data line, the status C bit is checked and the directory is used to identify a processing unit that has cached the data line. The request is transferred to the identified processing unit, and the data line is transferred from that processing unit to the processing unit that has issued the request. If a processing unit that has cached the data line has replaced the data line, it is checked if there is a processing unit that has cached the data line. If there is none, the data line is written back into the one partial main memory. If there is, the data line is not written back. Another status bit RO is also used for each data line. It indicates if the data line is read only. If a data line is read only, generation of the directory and storing it in the partial main memory is prohibited.