The site-percolation problem on a simple cubic lattice is studied by the Monte Carlo method. By combining results for periodic lattices of different sizes through the use of finite-size scaling theory we obtain good estimates forp c (0.3115±0.0005), (0.41±0.01), (1.6±0.1), and(0.8±0.1). These results are consistent with other studies. The shape of the clusters is also studied. The average surface area for clusters of sizek is found to be close to its maximal value for the low-concentration region as well as for the critical region. The percentage of particles in clusters of different sizesk is found to have an exponential tail for large values ofk forP p c. Forp >p c there is too much scatter in the data to draw firm conclusions about the size distribution.