The current paper discusses concepts for implementing distinct edge dislocations into continua. Such dislocation models are successful, if they correctly predict both the stress- and displacement field around the dislocation line and the driving force on the dislocation in the presence of an external stress state. In addition, it is desired to realize the dislocation model by finite element programs. It is shown that the dislocation models available in literature do not fulfill these conditions, since they do not yield the correct driving force terms. Additional defect structures are investigated in order to work out a more successful dislocation model. Several methods are applied to derive the driving force on the dislocation for each model, (i) the configurational force concept, (ii) a thermodynamic concept based on the interaction energy, (iii) a relationship based on conservation integrals and the dislocation density. The results are compared to the classical Peach-Koehler solution. Two different procedures are worked out to correctly model a single edge dislocation, a numerically very simple method in form of two strips with prescribed eigenstrain components, which are considered consecutively, and a numerically more sophisticated concept, denominated as “cut-displace-glue” procedure.