An external neutron source is necessary to start up and run a subcritical thermal nuclear reactor. The external neutron source can be a neutron generator, a radionuclide having spontaneous fission or an isotopic neutrons source. Turning off the neutron generator or removing the neutron source shuts down the reactor. In subcritical reactors for teaching, fuel tubes and items for irradiation can be inserted or removed even when the reactor is running because are radiological safe. The aim of this work was to estimate, using Monte Carlo methods, the neutron and γ-ray spectra at five sites outside a Subcritical thermal neutron reactor Nuclear Chicago model 9000 using water and polyethylene moderators. In addition, the ambient dose equivalent and the ambient dose, for neutrons and γ-rays were calculated. For neutrons, the ambient dose equivalent were calculated with the neutron fluence-to-ambient dose equivalent coefficients from the ICRP 74 and the neutron fluence-to-ambient dose response of the neutron area monitor LB 6411; while, the ambient dose was calculated using the ICRU 95 neutron fluence-to-ambient dose coefficients. For γ-rays, was calculated the ambient dose equivalent using the ICRP 74 photon fluence-to-ambient dose equivalent coefficients; while, the ambient dose was calculated with the photon fluence-to-ambient dose coefficients from the ICRU 95. Outside the reactor, neutron spectra have fast, epithermal and thermal neutrons, and gamma ray spectra have γ rays induced in the inelastic scattering and capture of neutrons with the reactor materials. Neutron and γ-ray fluence rates and dose rates are larger in the water-moderated reactor. The ambient dose rates, due to neutrons and γ-rays, are smaller than the ambient dose equivalent, because the ambient dose resembles the maximum effective dose.