Following Tomita and Murakami (Research of Pattern Formation ed R Takaki (Tokyo: KTK Scientific Publishers) pp 197–203) we propose an analytical model to predict the critical probability of percolation. It is based on the excursion set theory which allows us to consider N-dimensional bounded regions. Details are given for the three-dimensional (3D) case and statistically representative volume elements are calculated. Finally, generalisation to the N-dimensional case is made.