Wave transmitting boundaries are used to truncate an infinite domain when analysing soil-structure interaction problems involving wave propagation using dynamic finite element analysis procedures. This facilitates analysing a problem in an infinite domain considering a finite domain with boundaries, which has the ability to absorb the waves propagating away from the finite domain without reflecting them. Simulating proper non-reflective conditions at the boundaries during a finite element analysis is therefore vital for the accuracy of numerical solutions. Numerous approaches have been introduced to simulate non-reflecting boundary conditions in the past few decades and the accuracy or the capacity to absorb waves propagating into these boundaries has improved over the years. This paper presents a review of wave transmitting boundaries found in the literature. The performance of several wave transmitting boundaries is investigated by simulating them using the finite element program ABAQUS.