In this research, we formulate a mathematical model to obtain elevator operating index, especially average waiting time. The users generated on each floor of the building installed elevator will occur with the Poisson distribution and the service time by the elevator will be the Exponential distribution. Given these, we create a mathematical model that calculates average wait time and elevator operating index based on queue and stochastic process. Then, we compare the operation index by computer simulation with the value obtained by the model. It will be given these, we create a mathematical model that calculates average wait time and elevator operating index based on queue and stochastic process. Then, we compare the operation index by computer simulation with the value obtained by the model.