The recent developments in tubular laser cutting technologies provide a fast and very precise solution by combining several different steps—as 3D geometrical control of the beveled surface, laser-beam inclination, laser-beam power—in one operation cycle. Examples of joints and cuts by laser technology give an insight into what is possible. New types of K-joints made of rectangular hollow sections using different kind of gusset plates which make use of the advantages of laser cutting are in the focus of this investigation here. In a first step the resulting stress concentration factors SCF of classical K-joints with gap and without gusset plates are compared with new innovative joint geometries. For this comparison Finite element analysis is used.