Buckled graphene has potential applications in energy harvest, storage, conversion, and hydrogen storage. The investigation and quantification analysis of the random porosity in buckled graphene not only contributes to the performance reliability evaluation, but it also provides important references for artificial functionalization. This paper proposes a stochastic finite element model to quantify the randomly distributed porosities in pristine graphene. The Monte Carlo stochastic sampling process is combined with finite element computation to simulate the mechanical property of buckled graphene. Different boundary conditions are considered, and the corresponding results are compared. The impacts of random porosities on the buckling patterns are recorded and analyzed. Based on the large sampling space provided by the stochastic finite element model, the discrepancies caused by the number of random porosities are discussed. The possibility of strengthening effects in critical buckling stress is tracked in the large sampling space. The distinguishable interval ranges of probability density distribution for the relative variation of the critical buckling stress prove the promising potential of artificial control by the atomic vacancy amounts. In addition, the approximated Gaussian density distribution of critical buckling stress demonstrates the stochastic sampling efficiency by the Monte Carlo method and the artificial controllability of porous graphene. The results of this work provide new ideas for understanding the random porosities in buckled graphene and provide a basis for artificial functionalization through porosity controlling.