Integral experiments that measure the transport of ∼14-MeV deuterium-tritium (D-T) neutrons through laminated slabs of proposed fusion reactor shield materials have been carried out at the Oak Ridge National Laboratory. Measured and calculated neutron and gamma-ray energy spectra are compared as a function of the thickness and composition of Type 304 stainless steel, borated polyethylene (BP), and Hevimet (a tungsten alloy), and as a function of detector position behind these materials. The measured data were obtained by means of an NE-213 liquid scintillator using pulse-shape discrimination methods to resolve neutron and gamma-ray pulse-height data and spectral unfolding methods to convert these data to energy spectra. The calculated data were obtained using two-dimensional discrete-ordinates radiation transport methods in a complex calculational network that takes into account the energy-angle dependence of the D-T neutrons and the nonphysical anomalies of the Sn method. The transport calculations incorporate ENDF/B-IV cross-section data from the VITAMIN C data library. The measured and calculated neutron energy spectra are in good agreement behind slab configurations of Type 304 stainless steel and BP (∼10% for all neutron energies >850 keV). When 5 cm of Hevimet are added to a 45-cm-thick Type 304 stainless steel plus BP slab assembly, the agreement is less favorable. The agreement among the measured and calculated gamma-ray spectra for energies >750 keV ranges from ∼25% to a factor of ∼5 depending on the slab composition.