One of the fundamental characteristics of Cloud Computing is its elasticity. It is about the ability to dynamically adapt computer resources consumption to workload while maintaining performance and quality of service. Most current industrial as well as academic solutions have limitations in terms of elasticity control, which affects the availability and performance of systems. In this paper, we propose a modeling of an elastic Cloud platform in terms of the markovian queuing model where the number of active servers depends on the current workload. A quantitative analysis of the steady state of our model allows to analyze and calculate the value of the elasticity in a precise way.