Cloud applications have been gaining popularity in recent years for their flexibility in resource provisioning according to Web application demands. The Elastic Application Container (EAC) system is a technology that delivers a lightweight virtual resource unit for better resource efficiency and more scalable Web applications in the Cloud. It allows multiple application providers to concurrently run their Web applications on this technology without worrying the demand change of their Web applications. This is because the EAC system constantly monitors the resource usage of all hosting Web applications and automatically reacts to the resource usage change of Web applications (i.e. it automatically handles resource provisioning of the Web applications, such as scaling of the Web applications according to the demand). In the chapter, the authors firstly describe the architecture, its components of the EAC system, in order to give a brief overview of technologies involved in the system. They then present and explain resource-provisioning algorithms and techniques used in the EAC system for demand-driven Web applications. The resource-provisioning algorithms are presented, discussed, and evaluated so as to give readers a clear picture of resource-provisioning algorithms in the EAC system. Finally, the authors compare this EAC system technology with other Cloud technologies in terms of flexibility and resource efficiency.