This paper presents a scalable parallelization of an Eulerian–Lagrangian method, namely the three-dimensional front tracking method, for simulating multiphase flows. Operating on Eulerian–Lagrangian grids makes the front tracking method challenging to parallelize and optimize because different types of communication (Lagrangian–Eulerian, Eulerian–Eulerian, and Lagrangian–Lagrangian) should be managed. In this work, we optimize the data movement in both the Eulerian and Lagrangian grids and propose two different strategies for handling the Lagrangian grid shared by multiple subdomains. Moreover, we model three different types of communication emerged as a result of parallelization and implement various latency-hiding optimizations to reduce the communication overhead. Good scalability of the parallelization strategies is demonstrated on two supercomputers. A strong scaling study using 256 cores simulating 1728 interfaces or bubbles achieves 32.5x speedup. We also conduct weak scaling study on 4096 cores simulating 27,648 bubbles on a 1024×1024×2048 Eulerian grid resolution.