The biological effects of chronic ionizing radiation exposure can be difficult to study, but important to understand in order to protect the health of occupationally-exposed persons and victims of radiological accidents or malicious events. They include targeted effects (TE) caused by ionizations within/close to nuclear DNA, and non-targeted effects (NTE) caused by damage to other cell structures and/or activation of stress-signaling pathways in distant cells. Data on radiation damage in animal populations exposed over multiple generations to wide ranges of dose rates after the Chernobyl nuclear-power-plant accident are very useful for enhancing our understanding of these processes. We used a mechanistically-motivated mathematical model which includes TE and NTE to analyze a large published data set on chromosomal aberrations in pond snail (Lymnaea stagnalis) embryos collected over 16 years from water bodies contaminated by Chernobyl fallout, and from control locations. The fraction of embryo cells with aberrations increased dramatically (>10-fold) and non-linearly over a dose rate range of 0.03-420 μGy/h (0.00026-3.7 Gy/year). NTE were very important for describing the non-linearity of this radiation response: the TE-only model (without NTE) performed dramatically worse than the TE+NTE model. NTE were predicted to reach ½ of maximal intensity at 2.5 μGy/h (0.022 Gy/year) and to contribute >90% to the radiation response slope at dose rates <11 μGy/h (0.1 Gy/year). Internally-incorporated 90Sr was possibly more effective per unit dose than other radionuclides. The radiation response shape for chromosomal aberrations in snail embryos was consistent with data for a different endpoint: the fraction of young amoebocytes in adult snail haemolymph. Therefore, radiation may affect different snail life stages by similar mechanisms. The importance of NTE in our model-based analysis suggests that the search for modulators of NTE-related signaling pathways could be a promising strategy for mitigating the deleterious effects of chronic irradiation.