Containers emerged as cloud resource offerings. While the advantages of containers, such as easing the application deployment, orchestration and adaptation, work well for stateless applications, the feasibility of containerization of stateful applications, such as database management system (DBMS), still remains unclear due to potential performance overhead. The myriad of container operation models and storage backends even raises the complexity of operating a containerized DBMS. Here, we present an extensible evaluation methodology to identify performance overhead of a containerized DBMS by combining three operational models and two storage backends. For each combination a memory-bound and disk-bound workload is applied. The results show a clear performance overhead for containerized DBMS on top of virtual machines (VMs) compared to physical resources. Further, a containerized DBMS on top of VMs with different storage backends results in a tolerable performance overhead. Building upon these baseline results, we derive a set of open evaluation challenges for containerized DBMSs.