Cloud environments are being increasingly used for deploying and executing business processes and particularly Service-based Business Processes (SBPs). One of the expected features of Cloud environments is elasticity at different levels. It is obvious that provisioning of elastic platforms is not sufficient to provide elasticity of the deployed business process. Therefore, SBPs should be provided with elasticity so that they would be able to adapt to the workload changes while ensuring the desired functional and non-functional properties. In this paper, we propose a formal model for stateful SBPs elasticity that features a duplication/consolidation mechanisms and a generic controller to define and evaluate elasticity strategies.