The absorption probability of neutrons in a cylindrical sample is considered. The neutron beam is monochromatic and collimated, and its intensity is uniform across the beam. A uniform (one-region) sample and a nonuniform (concentric two-region) sample are considered. An exact solution in an analytic form is found for the uniform case. In the nonuniform case, the exact solution is given in the form of an integral (which should be numerically integrated). In the nonuniform sample, concave (i.e., low in the center) and convex distributions of absorber are considered. Some symmetry in the change in the absorption probability due to the absorber nonuniformity with respect to these types of absorber distributions is pointed out and discussed. The applicability and limitations of the solutions are discussed, and an application example is given.