Extreme flood events have occurred recently in Europe and in other parts of the world. The general concern of the scientific community is that the severity and frequency of such events have changed over time due to climate and environmental change, and they are further expected to change in the future. For these reasons, understanding the mechanisms of flood change and quantifying the sensitivity of floods to their drivers (i.e., the elasticities) are crucial aspects for flood risk management. In this study we investigate flood-change mechanisms with a model-based approach. First, we develop a probabilistic flood-change model, that captures the mechanisms of change separately, with the aim to understand the impact of different mechanisms of change in a more transparent way than by traditional scenario analyses. The mechanisms of change represented in the model, are: (i) the increase of the snow fall line due to higher air temperatures; (ii) the shortening of the snow melt period and shift in the seasonality of floods; (iii) lower soil moisture due to increased evaporation; (iv) changes in seasonal precipitation totals; (v) increasing fraction of convective precipitation; and (vi) land-cover changes. The model is based on derived distribution theory and relates the probabilities of the drivers to those of the floods via the mechanisms. Second, we calibrate the flood-change model simultaneously to flood and driver data from selected catchments in Europe. The calibration is carried out in the signature domain using Approximate Bayesian Computation (ABC). The advantages of using ABC for model calibration are that it does not require the evaluation of the likelihood function (which is often not available in closed form), and it allows us to take into account prior information about model parameters. From the calibrated model, we derive the elasticities of floods to the considered drivers for several catchments in Europe.