In executing data processing operations, a data processing system has a physical memory that is divided into a plurality of physical memory zones, each corresponding to a contiguous series of physical page numbers (NPP). A physical memory allocation method, in response to a request from a current process, activates a first function (Resa) which checks the number of available pages in a memory zone that iii distinguished from other memory zones by a name (z) specified by the current process and places the current process in a queue that corresponds to the zone designated (z) if the number of available pages is not sufficient in the zone designated (z), and then activates a second function (Allocate) which extracts a physical page number (NPP) from a list of available pages in the zone identified by the name (z) so that it can be used by the current process.