Induction thermography is a non-contacting, non-destructive evaluation method with a wide range of applications. A deeper understanding of the detectability of cracks requires fundamental knowledge about the induced current density distribution in the component under test. A calculation of the current distribution provides information how much current is flowing at which location of the component, how a crack disturbs the current density, how much heat is produced at which location of the component, and how the heat diffuses to the surface. The heating process depends on the type of crack. On the one hand there are cracks which can be detected mainly by direct observation of the heating process due to an increased current density, and on the other hand there are cracks which can be detected mainly because of a modification of the heat diffusion. This paper presents an analytical model for the calculation of the current distribution, including the back-flow current along with finite-element calculations. Furthermore, two new crack models are presented for a better description of real cracks.