The execution of parallel applications, using grid computing, requires an environment that enables them to be executed, managed, scheduled and monitored. The execution environment must provide a processing model, consisting of programming and execution models, with the objective appropriately exploiting grid computing characteristics. This paper proposes a parallel processing model, based on shared variables for grid computing, consisting of an execution model that is appropriate for the grid and a CPAR parallel language programming model. The environment is designed to execute parallel applications in grid computing, where all the characteristics present in grid computing are transparent to users. The results show that this environment is an efficient solution for the execution of parallel applications.