Spectral measurements of intermediate-energy neutrons (i.e., En ≤ 65 MeV) transmitted through iron, lead, graphite, and concrete shields are described. Concurrently, transmitted spectra of associated gamma rays are also obtained. A collimated beam of neutrons induced by 65-MeV protons in a thick copper target is utilized in the measurements. Measurements of both neutrons and gamma rays penetrating the shields are by an NE-213 scintillator. Monte Carlo calculations using the MORSE code are carried out with the DLC-87 Hilo multigroup cross sections. For neutron spectra, comparison between the measured and calculated spectra indicates that the DLC-87 data reproduce the measured data well for the graphite and the concrete shields but give only slightly higher values at energies of 15 to 30 MeV for the iron shield and overpredict the lead-transmitted spectra. Tests on the cross sections reveal that the underestimation of the total iron cross section by the DLC-87 in the 15- to 25-MeV energy range is the reason for the overestimation of the iron transmitted spectra. Neglecting the elastic scattering in evaluating the lead data is the reason for the large overestimation of the lead transmitted spectra. Gamma-ray spectra obtained behind the graphite and concrete shields are well explained by the transmission of source gamma rays from the copper target through the shields. However, the intensity of the measured photons behind iron and lead shields is much larger than that of transmitted source photons. The discrepancies are not explained by including neutron-induced gamma rays for neutrons from thermal energy up to 15 MeV. The gamma-ray production cross-section data may be required for neutrons >15 MeV to explain the remaining large discrepancies.