The proliferation of genetically modified crops has created a need for methods to predict the likelihood of gene introgression into related species in situ. We present a model of a modified crop and an associated unmodified plant population removed spatially from the modified crop but not completely isolated from it, reflecting standard practices for isolation of field trials. We develop models for two kinds of life histories, broadly based on Brassica and Gossypium, taxa that are targets for genetic modification. We find that current prescriptions for field trials are likely to lead to escape of transgenes into wild populations when outcrossing rates are moderate and hybrids are fertile. The results are sensitive to pollen rain within plausible bounds for model parameters, suggesting buffer widths are an important aspect of the design of field trials. When gene introgression requires the spontaneous development of a polyploid, the likelihood of gene introgression is lower but still appreciable in realistic circumstances. Events that are unlikely over periods of a few years become almost certain within scales of a few decades, emphasising the need for gene risk assessments to be set in specified time frames. The models serve to identify the parts of the system that are poorly known and that are important in determining outcomes, providing a focus for future research. There is a need for research on the consequences of changes in fitness due to the transgenes, competitive interactions between related species, and the broader ecological consequences of changes in agricultural practice resulting from the use of genetically modified crops.