The three parameter Crack distribution is a mixture of the two parameter Inverse Gaussian distribution and Length Biased Inverse Gaussian distribution and Birnbaum-Saunders distribution is a special case for p = 1 2 ; where 0 p 1, is the weight parameter. In this thesis, we have developed and investigated estimation method and procedures in order to estimate parameters of the Crack distribution. First we focused on the derivation of the Moment Generating Function to construct a new method in order to find the first four raw moments, which are used to estimate parameters by Method of Moments. For illustration purpose we considered four real data sets, which indicated the goodness of fit and flexibility of the Crack model. In addition, we proposed composition method to generate Crack random number and developed algorithm and estimation procedure to estimate parameters in order to calibrate Bias, Variance and Mean Square Error. Results of the simulation are presented numerically and graphically for various scenarios to compare the performance of the Method of Moments and Maximum Likelihood Estimates. The shape of the Crack density functions are also illustrated graphically for some specific values of parameters. The simulated and real data are studied by using Excel and Matlab.