Cloud computing is a new model for the provisioning of dynamically elastic and often virtualized resources at the levels of infrastructures, platforms and software. Cloud platforms are being increasingly used for the deployment and execution of service-based business processes (SBPs). Nevertheless, the provisioning of elastic infrastructures and/or platforms is not sufficient to provide users with elasticity at the level of SBPs. Therefore, there is a need to provide SBPs with mechanisms to scale their resource requirements up and down whenever possible. This can be achieved using mechanisms for duplicating and consolidating business services that compose the SBPs. In this paper, we propose a formal model and a generic framework for elasticity of SBPs.