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Elasticity is a key feature of cloud computing. Its application has become an increasing need due to the dynamic nature of different applications and different workloads imposed by them. This article aims to analyze the behavior of the elasticity in a cloud computing environment, based on some metrics related to response time of allocation operations and used resources in a cloud computing environment. A proposal of seven metrics for evaluation of the elasticity is presented. An experiment to validate the proposal and analysis of elasticity in a cloud computing environment is described with microbenchmarks and a scientific application. At the end, a discussion of the results and future work.