An abstract machine for parallel graph reduction on a shared memory multiprocessor is described. This is intended primarily for normal order (lazy) evaluation of functional pro-grams. It is absolutely essential in such a design to adapt an efficient sequential model since during execution under limited resources available, performance will be reduced in the limit to that of the sequential engine. Parallel evaluation of normal order functional languages performed naively can result in poor overall performance despite the availability of sufficient processing elements and parallelism in the application. Needless context switching, task migration and continuation building may occur when a sequential thread of control would have sufficed. Furthermore, the compiler using static information cannot be fully aware of the availability of resources and their optimal utilization at any moment in run time. Indeed this may vary between runs which further aggravates the job of the compiler writer in generating optimal and compact code for programs. The benefits derived from this model are: 1) it is based on the G-machine so that execution under limited resources will default to a performance close to that of the G-machine; 2) the additional instructions needed to control the complexities of parallel evaluation are extremely simple, almost trivializing the job of the compiler writer; 3) attempts are made where possible to avoid context switching and task migration by retaining a sequential thread of control (made more clear in the paper), and 4) the method has demonstrated good overall performance on a shared memory multiprocessor.