Aneurysm rupture occurs when local wall stresses exceed the tensile strength of vascular tissues. Knowledge of vascular wall stresses, and insight into the factors that change wall stresses, will lead to a better understanding of how aneurysms grow and rupture. In this study, stress distributions in the walls of small aneurysms were calculated using finite element analysis (FEA), a numerical technique able to predict stress distributions with greater accuracy than the Law of Laplace. Stresses were calculated for an initial small aneurysm and compared to stresses produced by increasing the aneurysm diameter, decreasing the wall thickness, and changing the material properties of the aneurysm wall. FEA calculations indicate that wall stresses are generally greatest on the inner surface of an aneurysm, and decrease nonlinearly as the outer wall is approached. Maximum wall stresses occur along the region of greatest diameter, and circumferential stresses tend to be significantly greater than longitudinal stresses. Doubling the diameter of an aneurysm produced a twofold increase in the maximum wall stress. Decreasing the wall thickness by half also produced a doubling of the maximum wall stress. Changing material properties produced no appreciable change in wall stresses. However, weaker materials fail at lower stresses, thus halving material strength would be equivalent to doubling wall stresses. We conclude that the Law of Laplace is inaccurate in predicting the complicated stress distributions that exist in aneurysm walls, and that more sophisticated tools, such as FEA, will be needed to understand this complex phenomenon. We also conclude that proportional changes in the diameter, wall thickness, or aneurysm tissue strength have roughly equivalent effects on aneurysm growth and rupture.