We present physical/mathematical models base on partial differential equations (PDEs) and efficient numerical simulation schemes based on the Finite Element (FE) method for multi-field problems, where the acoustic field is the field of main interest. Acoustics, the theory of sound, is an emerging scientific field including disciplines from physics over engineering to medical science. We concentrate on the following three topics: vibro-acoustics, aero-acoustics and high intensity focused ultrasound. For each topic, we discuss the physical/mathematical modeling, efficient numerical schemes and provide practical applications.