Atmospheric science is advancing towards very complex phenomena at ever smaller temporal and spatial scales. One of the principal tools utilized in atmospheric science are weather prediction models. These models usually demand large execution times and resource allocation, such as CPU time and storage space. The main goal of our research is porting of the Weather Research and Forecasting model to the Grid infrastructure. Porting has been done through bash scripts that are using existing Grid tools for job and data management, authentification mechanisms, and other application level services produced within the SEEGRID project. In this paper, through a few model runs on the Grid we describe certain benefits not only in the overall execution time but also in the ability of performing concurrent runs of the same model especially for scientific purposes. During the execution, we have also faced some drawbacks in data bandwidth, unreliability of some Grid services and relatively hard control of the model execution flow. The final conclusion is that there is a big need and justification for porting the WRF model to the Grid, although it takes a lot of effort to be properly implemented.