A comprehensive understanding of the lunar radiation environment is essential in preparing for future human exploration of the Moon. The radiation environment on the Moon includes primary space radiation and secondary radiation, which is induced in the lunar soil. Both primary and secondary radiation may pose severe health issues to future crews on the Moon. In this work, we build a detailed radiation environment model “Radiation Environment and Dose at the Moon (REDMoon)” for the lunar surface and subsurface. We use the GEANT4 (GEometry ANd Tracking) Monte‐Carlo code and “response function” approach to calculate type‐, energy‐, angular‐, depth‐, and time‐dependent particle spectra induced by galactic cosmic rays at the surface and subsurface of the Moon. Calculated radiation particle fluxes on and beneath the surface are in good agreement with previous experimental and numerical results while offering more details on the lunar radiation fields, such as angular and depth information. The depth profile of secondary particle spectra in the lunar soil has a maximum between 0.5 and 1 m below the surface, depending on particle type and energy. The angular distribution of secondary particles (in particular neutron, γ‐rays, electrons) with energy ≲1 MeV is mostly isotropic, while higher energy particles preferentially propagate downward. Our model provides full coverage of the spatial, directional, and energy information of the radiation field at the surface and subsurface of the Moon, which can serve for designing future human bases on the Moon.