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We use a Domain Specific Language (DSL) based on UML activity diagrams (UML-AD) to specify and compose systematically workflow models from Grid services. To be executed, workflow activity diagram models should be translated into BPEL4WS models which will be executed by the BPEL4WS engine. To reach this objective, we propose a meta-model based transformation from UML activity diagrams to BPEL4WS language. To ensure the correctness and the completion of the transformation, we propose a graph homomorphic mapping between the activity diagram and BPEL4WS language elements. To execute the BPEL4WS provided model, we propose in this paper an execution infrastructure based on The Globus Tool Kit.