UCMs (Use Case Maps) model describes functional requirements and high-level designs with causal paths superimposed on a structure of components. It could provide useful resources for software acceptance testing. However until now statistical testing technologies for large scale software is not considered yet in UCMs model. Thus if one applies UCMs model to a large scale software using traditional coverage based exhaustive tasting, then it requires too much costs for the quality assurance. Therefore this paper proposes an importance analysis of UCMs model with Markov chains. With this approach not only highly frequently used usage scenarios but also important objects such as components, responsibilities, stubs and plugins can also be identified from UCMs specifications. Therefore careful analysis, design, implementation and efficient testing could be possible with the importance of scenarios and objects during the full software life cycle. Consequently product reliability can be obtained with low costs. This paper includes an importance analysis method that identifies important scenarios and objects and a case study to illustrate the applicability of the proposed approach.