The abrasive waterjet is nowadays widely used especially for cutting hard and difficult to machine materials. However, achieving the desired surface quality of the material to be cut, which can be described by roughness (Ra) and waviness (Wa) values, is challenging and is related to the setting of the jet parameters. The traverse speed of the cutting head was selected as the most suitable parameter that can influence the roughness and waviness, as it has a direct economic impact in addition to influencing the surface quality. Therefore, the aim of this paper is to determine the effect of the traverse speed on roughness and waviness values. However, these also depend on the depth of cut and the effect of speed may be different for different depths. For this reason, the dependence of roughness and waviness on the depth of cut has also been considered. To investigate these effects, experiments were carried out on different materials. The results show that roughness and waviness are essentially constant for small depth of cut, then increasing non-linearly with increasing of the depth of cut. There is an increase in roughness and waviness with increasing traverse speed, but this also becomes apparent only from a certain depth. These conclusions apply to all materials, but material properties, such as hardness, have an effect on specific roughness values. Further research work will be carried out to find the specific dependence of roughness and waviness on the depth of cut and the traverse speed of the cutting head.