The angular and energy distributions of neutrons produced by 100 and 180 MeV/nucleon He and 100, 180, and 400 MeV/nucleon C ions stopping in thick C, Al, Cu, and Pb targets were measured using the Heavy-Ion Medical Accelerator in Chiba of the National Institute of Radiological Science (NIRS), Japan. The neutron spectra in the forward direction have broad peaks of ~60 to 70% of the incident particle energy per nucleon due to the break-up process, and they spread up to almost twice the projectile energy per nucleon. The neutron spectra are similar for the same incident energy of 100 MeV/nucleon for both He and C ions. The phenomenological hybrid analysis, based on the moving source model and the Gaussian fitting of the break-up process, could well represent the measured thick target neutron spectra. The experimental results are also compared with the calculations using the heavy-ion code, and the calculated results agree with the measured results within a factor of 2 margin of accuracy. This systematic study on neutron production from thick targets by high-energy heavy ions is the first experimental work performed by NIRS and will be useful for designing the shielding for the high-energy heavy-ion accelerator facility.