High Performance Fortran (HPF) has emerged as a standard language fordata parallel computing. However, a wide variety of scientific applications are best programmed by a combination of task and data parallelism. Therefore, a good model of task parallelism is important for continued success of HPF for parallel programming. This paper presents a task parallelism model that is simple, elegant, and relatively easy to implement in an HPF environment. Task parallelism is exploited by mechanisms for dividing processors into subgroups and mapping computations and data onto processor subgroups. This model of task parallelism has been implemented in the Fx compiler at Carnegie Mellon University. The paper addresses the main issues in compiling integrated task and data parallel programs and reports on the use of this model for programming various flat and nested task structures. Performance results are presented for a set of programs spanning signal processing, image processing, computer vision and environment modeling. A variant of this task model is a new approved extension of HPF and this paper offers insight into the power of expression and ease of implementation of this extension.