Non-targeted (bystander) effects of ionizing radiation are caused by intercellular signaling; they include production of DNA damage and alterations in cell fate (i.e. apoptosis, differentiation, senescence or proliferation). Biophysical models capable of quantifying these effects may improve cancer risk estimation at radiation doses below the epidemiological detection threshold. Understanding the spatial patterns of bystander responses is important, because it provides estimates of how many bystander cells are affected per irradiated cell. In a first approach to modeling of bystander spatial effects in a three-dimensional artificial tissue, we assume the following: (1) The bystander phenomenon results from signaling molecules (S) that rapidly propagate from irradiated cells and decrease in concentration (exponentially in the case of planar symmetry) as distance increases. (2) These signals can convert cells to a long-lived epigenetically activated state, e.g. a state of oxidative stress; cells in this state are more prone to DNA damage and behavior alterations than normal and therefore exhibit an increased response (R) for many end points (e.g. apoptosis, differentiation, micronucleation). These assumptions are implemented by a mathematical formalism and computational algorithms. The model adequately describes data on bystander responses in the 3D system using a small number of adjustable parameters.