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Appropriate mapping procedures make heterogeneous computing environment especially suitable for the execution of various computer-intensive applications. The paper shows a static dynamic mapping procedure relying on the multicriteria model. Model parameters describe the application, platform, mapping and user. They are divided into static and dynamic ones with three weight levels assigned to them. The described approach ensures optimal initial mapping, but also a quick response to changes in the environment, which is supported by prediction. The described approach is a simplified environment shows improvements in the execution of the test application. Further adjustments are directed towards the implementation in the computational grid.