A detailed Monte Carlo analysis in one, two, and three dimensions and with different multigroup scattering kernels is presented for a number of actual reactor systems. Several variance reducing sampling techniques, which we believe to be unusual, are employed and, in addition to the prediction of reactivity, much emphasis is placed on generation time calculations with reference to the “life cycle” point of view. One of the main points of interest in the numerical results obtained is the comparison of the reactivity and time eigenvalues with those obtained from the equivalent SN and jN calculations. The excellent agreement with these two methods establishes the necessary confidence in the Monte Carlo procedure described here. As a further illustration of the method, it was thought to be of interest to compare the numerical results obtained from different scattering kernels (transport approximation, linear anisotropy, and exact anisotropy) with a view to assessing the influence of these different approximations on the reactivity, absorption, leakage, generation time, etc. Simultaneously, an examination of two different Monte Carlo sampling techniques is presented. To apply a physical test to the method, some highly enriched uranium spheres, some cylinders of extreme geometry reflected by a variety of materials, and some cylindrical annuli were analyzed and the results compared with experiments. In addition, some systems requiring the full use of the three-dimensional scope of the method are studied. The efficiency of the Monte Carlo procedure is finally illustrated by listing, for several calculations, the probable errors in the reactor eigenvalues and other parameters after 10 min of IBM-7090 computer time. This analysis proves that statistical methods can be used to carry out threedimensional assessments of reactor assemblies with sufficient accuracy without the expenditure of a prohibitive amount of computer time. Such a goal has not yet been achieved by the numerical or analytical methods which solve the neutron transport equation.