The three parameter Crack distribution is useful for statistical analysis in prospective studies connected with the engineering problem of fatigue crack development in a metallic plate under some kind of pressure loading. As special cases it contains such well known distributions as the Birnbaum-Saunders distribution, the Inverse Gaussian distribution, and the Length Biased Inverse Gaussian distribution. These distributions are all related and have their own characteristics. In this thesis, in Chapter 2, I derive new, more direct and more mathematically appealing methods for obtaining the distribution function and the moment generating function for the Crack distribution. In Chapter 3 I provide new probability properties of the Crack distribution. Finally, in Chapter 4 I provide a rigorous general probabilistic model of the growth of two-sided cracks.