Many books in statistics which concerned with the life time distributions does not give sufficient details on the study of c.d.f. of gamma distribution and its tabl So in mis thesis, we consider an approach which approximate the cumulative density function as a limit sum. Further discussion of the approximation of incomplete gamma integral, as well as we consider the approximation of gamma function and its higher derivatives. Tables of the above approximation are represented by the aid of the computer programs. Also we study several procedures for generating random variates from gamma distribution, and the efficiency for each procedure is developed theoretically and assist practically by Monte Carlo simulation, also we record die time needed for each generation. Finally table of comparison between these procedures presents.