Bayesian theory of model calibration provides a coherent framework for distinguishing and encoding multiple sources of uncertainty in probabilistic predictions of flooding. This paper demonstrates the use of a Bayesian approach to computer model calibration, where the calibration data are in the form of spatial observations of flood extent. The Bayesian procedure involves generating posterior distributions of the flood model calibration parameters and observation error, as well as a Gaussian model inadequacy function, which represents the discrepancy between the best model predictions and reality. The approach is first illustrated with a simple didactic example and is then applied to a flood model of a reach of the river Thames in the UK. A predictive spatial distribution of flooding is generated for a flood of given severity.