Cosmic radiation is the most serious risk that will be encountered during the planned missions to the Moon and Mars. There is a compelling need to understand the effects, safety thresholds, and mechanisms of radiation damage in human tissues, in order to develop measures for radiation protection during extended space travel. As animal models fail to recapitulate the molecular changes in astronauts, engineered human tissues and "organs-on-chips" are valuable tools for studying effects of radiation in vitro. We have developed a bioengineered tissue platform for studying radiation damage in individualized settings. To demonstrate its utility, we determined the effects of radiation using engineered models of two human tissues known to be radiosensitive: engineered cardiac tissues (eCT, a target of chronic radiation damage) and engineered bone marrow (eBM, a target of acute radiation damage). We report the effects of high-dose neutrons, a proxy for simulated galactic cosmic rays, on the expression of key genes implicated in tissue responses to ionizing radiation, phenotypic and functional changes in both tissues, and proof-of-principle application of radioprotective agents. We further determined the extent of inflammatory, oxidative stress, and matrix remodeling gene expression changes, and found that these changes were associated with an early hypertrophic phenotype in eCT and myeloid skewing in eBM. We propose that individualized models of human tissues have potential to provide insights into the effects and mechanisms of radiation during deep-space missions and allow testing of radioprotective measures.