In this thesis the creation of discrete transparent boundary conditions (DTBC´s) for parabolic wave equations (PE´s) in underwater acoustics is treated. The DTBC´s are obtained by using analytical solutions to PE´s for a semi-infinite and homogeneous bottom. These new boundary conditions have been compared with the method of damping layers, which until recently was the common way to truncate an infinite bottom. Three testing examples were used for the evaluation: the lloyd mirror, the Bucker wave-guide and the Jensen-Kuperman wedge. The DTBC´s showed to be much more time efficient and correct than the damping layer method. A first display of the functionality of the DTBC can be seen on the front page, which shows the evolution of a beam hitting a wedge shaped prism in a homogeneous water half-space. As seen from the figure the part of the beam that encounters the surface is reflected back while the bottom bounary is transparent.