The primary particles entering the upper atmosphere as cosmic rays create showers in the atmosphere that include a broad spectrum of secondary neutrons, muons and protons. These cosmic ray secondaries interact with materials at the surface of the Earth, yielding prompt backgrounds in radiation detection systems, as well as inducing long-lived activities through spallation events, dominated by the higher-energy neutron secondaries. For historical reasons, the multiple neutrons produced in spallation cascade events are referred to as "ship effect" neutrons. Quantifying the background from cosmic ray induced activities is important to lowbackground experiments, such as neutrinoless double-beta decay.Since direct measurements of the effects of shielding on the cosmic ray neutron spectrum are not available, Monte Carlo modeling is used to compute such effects. However, there are large uncertainties (orders of magnitude) in the possible cross-section libraries and the cosmic ray neutron spectrum for the energy range needed in such calculations.The measurements reported here were initiated to validate results from Monte Carlo models through experimental measurements in order to provide some confidence in the model results.The results indicate that the models provide the correct trends of neutron production with increasing density, but there is substantial disagreement between the models and experimental results for the lower-density materials of Al, Fe and Cu.