The two-parameter crack lifetime distribution had led to the development of the three-parameter crack lifetime distribution. The developments has been a very use- ful and e ective tool in statistical analysis in conjunction with engineering concept relating to the fatigue crack which usually happen in the materials used for most engineering products like lorry, air craft and other heavy machineries. The crack is said to occur when excessive load or force is exerted beyond the materials ability or tendency. This three-parameter crack lifetime distribution was developed from the already-known two-parameter distributions, which was also used for modeling fatigue failure. This two-parameter lifetime distribution includes: Length-biased Inverse Gaussian distributions, the Birnbaum-Saunders distribution and also the Gaussian distribution. There is a strong relationship between the two-parameter distributions and the three-parameter lifetime distribution. However, there has not been much literature on the generation of the crack random numbers that follow the three-parameter crack distribution. The research brie y explains a few issues in generating random numbers. The research consider some values of the proposed parameter in this research for the simulation procedure and make the comparison by the generated histograms using the Software package R. The values of these parameters are = 2, 5, 10, 20, = 1, 5, 10 and p = 0.2, 0.4, 0.6. There are two major ways of generating random numbers classi ed in this research as direct and in-direct approach. The non-direct approaches consist of the acceptance-rejection method, and the direct approach comprises of the convolution procedure, the inversion, the composite, and many other procedures. Some of the methods will be brie y reviewed in the second chapter of this thesis. The situation where the direct approach can not be e ciently used in the generation of the random variable then the Acceptance-Rejection approach is most likely to be used. The result of the generation procedure in this research is presented in histogram and compared.