Applications in science and engineering often require huge computational resources for solving problems within a reasonable time frame. Parallel supercomputers provide the computational infrastructure for solving such problems. A traditional application scheduler running on a parallel cluster only supports static scheduling where the number of processors allocated to an application remains fixed throughout the lifetime of execution of the job. Due to the unpredictability in job arrival times and varying resource requirements, static scheduling can result in idle system resources thereby decreasing the overall system throughput. In this paper we present a prototype framework called ReSHAPE, which supports dynamic resizing of parallel MPI applications executed on distributed memory platforms. The framework includes a scheduler that supports resizing of applications, an API to enable applications to interact with the scheduler, and a library that makes resizing viable. Applications executed using the ReSHAPE scheduler framework can expand to take advantage of additional free processors or can shrink to accommodate a high priority application, without getting suspended. In our research, we have mainly focused on structured applications that have two-dimensional data arrays distributed across a two-dimensional processor grid. The resize library includes algorithms for processor selection and processor mapping. Experimental results show that the ReSHAPE framework can improve individual job turn-around time and overall system throughput.