For many years it has been suggested that lava tubes on the Moon could provide an ideal location for a manned lunar base, by providing shelter from various natural hazards, such as cosmic radiation, meteorites, micrometeoroids, and impact crater ejecta, and also providing a natural environmental control, with a nearly constant temperature, unlike that of the lunar surface showing extreme variation in its diurnal cycle. An analysis of radiation safety issues on lunar lava tubes has been performed by considering radiation from galactic cosmic rays (GCR) and Solar Particle Events (SPE) interacting with the lunar surface, modeled as a regolith layer and rock. The chemical composition has been chosen as typical of the lunar regions where the largest number of lava tube candidates are found. Particles have been transported all through the regolith and the rock, and received particles flux and doses have been calculated. The radiation safety of lunar lava tubes environments has been demonstrated.