Induced travel is an important component of travel demand and increasing attention has been paid to building analytical model to get more precise travel demand forecasting. In general, induced demand can be defined in terms of additional trips that would be made if travel conditions improved (less congested, lower vehicle costs or tolls). In this paper the induced demand resulting from higher design speeds and, therefore by less travel time, for the High Speed 1 in UK will be modelled on the basis of the relationship between existing High Speed Rail demand (dependent variable) to existing High Speed Rail travel times and costs. The covariates include socioeconomic variables related to population and employment in the zones connected by the High Speed Rail services. This model has been calibrated by mean of a before and after study carried on the corridor, when the new High Speed Rail services was introduced. Elasticities of induced travel (trips and VMT) have been computed with respect to fares, travel time and service frequency.