Knowledge of epidemiological mechanisms and parameters underlying scrapie transmission in sheep flocks remains very limited at present. Here we introduce a method for fitting stochastic transmission models to outbreak data to estimate bounds on key transmission parameters. We apply this method to data describing an outbreak of scrapie in a closed flock of Romanov sheep. The main findings are that the relative infectiousness of infected animals in this outbreak becomes appreciable early into disease incubation and that the mean incubation period is less than 1·5 years. We also find that the data are consistent with a broad range of values for the basic reproduction number R0 and describe how the boundaries of this range depend on assumptions about the mean incubation period and the contribution to transmission of a long-lived environmental reservoir of infectivity.