This paper describes the design and implementation of virtual memory management within the CMU Mach Operating System and the experiences gained by the Mach kernel group in porting that system to a variety of architectures. As of this writing, Mach runs on more than half a dozen uniprocessors and multiprocessors including the VAX family of uniprocessors and multiprocessors, the IBM RT PC, the SUN 3, the Encore MultiMax, the Sequent Balance 21000 and several experimental computers. Although these systems vary considerably in the kind of hardware support for memory management they provide, the machine-dependent portion of Mach virtual memory consists of a single code module and its related header file. This separation of software memory management from hardware support has been accomplished without sacrificing system performance. In addition to improving portability, it makes possible a relatively unbiased examination of the pros and cons of various hardware memory management schemes, especially as they apply to the support of multiprocessors.