Explicit formulas are given one-velocity escape probabilities from absorbing and (isotropic) scattering slabs in vacuo as calculated by the methods of asymptotic reactor theory. The results are compared with exact numerical calculations, diffusion theory, and a variational principal. Even for slabs as thin as two mean free paths, the asymptotic calculations are found to be highly accurate. By comparing the asymptotic methods with some multiple-scattering calculations for infinite cylinders, an extrapolated boundary has been defined for the cylinder, and in this fashion explicit formulas have been obtained for the escape probabilities from finite cylinders.