Cost Damping is a feature in some travel demand models by which the marginal disutility of cost (and, possibly, of time) declines as journey lengths increase. It is present in many models in practical use in the UK and the Department for Transport sought recommendations for the advice it issues to local planners in the ‘WebTAG’ system: www.dft.gov.uk/webtag. The report makes a review of UK and limited international practice, a significant part of it due to RAND Europe, and discusses the advantages, disadvantages and theoretical backgrounds of the methods that are used, which can be reduced to eight principal model formulations, each in turn belonging to one of four essentially different types. Evidence of the importance of Cost Damping in practice is assessed. Tests of the model formulations are proposed, including a novel ‘kilometrage’ test, and a number of the model forms used in practice are found to be unsatisfactory with respect to one or other of these tests. The use of distance as a variable in the models is found to be unsatisfactory. The report goes on to show that microeconomic theory gives little insight into the appropriate forms of Cost Damping. Finally, a small number of Cost Damping mechanisms are recommended as being acceptable for use in practical modelling.