Subroutines are written to generate random numbers on the computer. Depending on the subroutine used, the generated random numbers follow the uniform, binomial, normal, chi-square, t, F, or gamma distribution. Each subroutine is tested using the chi-square goodness of fit test to verify that the random numbers generated by each subroutine follow the statistical distribution for which it is written. The interpretation of the test results indicates that each subroutine generates random numbers which closely approximates the theoretical distribution for which it is designed. The approach used in the subroutine which generates gamma distributed random numbers involves the use of numerical integration, whereas simpler techniques are used in all the other subroutines. Each subroutine is documented with a description of how to use it and an explanation of the methods used to obtain the random numbers which it is designed to generate. (77 pages)