MPI is a well-established technology that is used widely in high-performance computing environment. However, setting up an MPI cluster can be challenging and time-consuming. This paper tackles this challenge by using modern containerization technology, which is Docker, and container orchestration technology, which is Docker Swarm mode, to automate the MPI cluster setup and deployment. We created a ready-to-use solution for developing and deploying MPI programs in a cluster of Docker containers running on multiple machines, orchestrated with Docker Swarm mode, to perform high computation tasks. We explain the considerations when creating Docker image that will be instantiated as MPI nodes, and we describe the steps needed to set up a fully connected MPI cluster as Docker containers running in a Docker Swarm mode. Our goal is to give the rationale behind our solution so that others can adapt to different system requirements. All pre-built Docker images, source code, documentation, and screencasts are publicly available.