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In this paper we present the strategy of RUP process modeling by using various forms of UML activity diagram representations. Also we identify several deficiencies in this representation of the process. We have tried come up with a better solution so we have developed a new version of the RUP modeling representation of the business modeling, requirement, analysis and design, implementation, test, and deployment discipline diagrams using the diagramming technique called RAD. We then have analyzed this alternate representation and extended the RAD notation to include artifacts flow. We have named this extension of RAD, XRAD. We then have used XRAD to represent the above mentioned disciplines of the RUP. This proposed version will be particularly useful to process designers, who create the drafts of the process, but also to actual developers who implement the process. It is a useful tool to create simple diagrams that will look familiar to all process actors. The novelty of our modeling strategy consists of the development of several role activity diagrams (RAD) for the Business Modeling, Requirement Analysis and Design, Implementation, Test and Deployment disciplines, as an element of originality. Each RAD diagram is developed in two different versions in order to improve their structure and readability. The development of a new version for Business Modeling Requirements, Analysis and Design, Implementation, Test and Deployment disciplines, called XRAD, as a combination of the second version and the artifacts, which make them more attractive, expressive, and compact than original versions and represent another remarkable result of our research.