Threshold porosity above which fission gas release channels would be formed in the rim egion of high burnup UO$_2$ fuel was estimated by the Monte Carlo method and Hoshen-Kopelman algorithm. With the assumption that both rim pore and rim grain can be represented by cube, pore distribution in the rim was simulated 3-dimensionally by the Monte Carlo method according to porosity and pore size distribution. Then, using the Hoshen-Kopelman algorithm, the fraction of open rim pores interlinked to the outer surface of a fuel pellet was derived as a function of rim porosity. The simulation showed that porosity of 24-25% is the threshold above which the number of rim pores forming release channels increases very rapidly. On the other hand, channels would not be formed if the porosity is less than about 23.5%. This is consistent with the observation that, for porosity less than 23.5%, almost no fission gas is released in the rim. However, once the rim porosity reaches beyond 25%, extensive open paths would be developed and considerable fission gas release would start in the rim.