There are a number of approaches to the modeling of cracks in beam structures reported in the literature, that fall into three main categories; local stiffness reduction, discrete spring models, and complex models in two or three dimensions. This paper compares the different approaches to crack modeling, and demonstrates that for structural health monitoring using low frequency vibration, simple models of crack flexibility based on beam elements are adequate. This paper also addresses the effect of the excitation for breathing cracks, where the beam stiffness is bilinear, depending on whether the crack is open or closed. Most structural health monitoring methods assume that the structure is behaving linearly, whereas in practice the response will be nonlinear to an extent that varies with the form of the excitation. This paper will demonstrate these effects for a simple beam structure.