This paper proposes an architecture called Cont-MEC for enabling UEs (User Equipments) to offload a part of applications to MEC (Multi-access Edge Computing) servers. It is expected that a MEC infrastructure is composed of a small number of centralized data centers and geographically distributed edge stations, in each of which multiple edge servers are installed. It is also expected that applications on UEs are implemented as container clusters similar to cloud-native applications and they are deployed on computing clusters. ContMEC has the following three features: (i) constructing a computing cluster per edge station for scalability to the number of UEs, (ii) hierarchical resource management for scalability and efficient resource sharing among computing clusters, and (iii) overlapped computing clusters for efficient resource sharing. A PoC (Proof-of Concept) implementation of ContMEC employs Kubernetes as a container orchestration system without modifications although Kubernetes does not take account of the MEC infrastructure. The PoC implementation shows that advantage of offloading is larger than disadvantage of implementing applications as container clusters, control traffic is moderate against the number of UEs, and efficient resource sharing among computing clusters is achieved.