Variations in High Performance Computing (HPC) system software configurations mean that applications are typically configured and built for specific HPC environments. Building applications can require a significant investment of time and effort for application users and requires application users to have additional technical knowledge. Linux container technologies such as Docker and Charliecloud bring great benefits to the application development, build and deployment processes. While cloud platforms already widely support containers, HPC systems still have non-uniform support of container technologies. In this work, we propose a unified runtime framework -- Build and Execution Environment (BEE) across both HPC and cloud platforms that allows users to run their containerized HPC applications across all supported platforms without modification. We design four BEE backends for four different classes of HPC or cloud platform so that together they cover the majority of mainstream computing platforms for HPC users. Evaluations show that BEE provides an easy-to-use unified user interface, execution environment, and comparable performance.