Abstract: In this paper, we analyze the performances of the random linear network coding (RLNC) based wireless broadcasting system, where a source wants to broadcast N packets to a large number of users with uniform distribution. By resorting to stochastic geometry analysis, we deduce the approximate average number of transmissions and the average percent of successful decoding users in the RLNC based wireless broadcasting system. Simulation results are given to demonstrate the accuracy of our theoretical analyses and the performance improvement of using RLNC scheme when compared with LT codes( Luby Transform codes). Meanwhile, we show that a user can recover all the original packets with high probability by receiving N out of all the transmitted RLNC combined packets.