In this paper we investigate the within-host dynamics of the foot-and-mouth disease virus (FMDV) in cattle using previously published data for 8 experimentally infected cows. An 8-compartment, 14-parameter differential equation model was fitted to data collected from each cow every 24h over the course of an infection on: (i) the concentration of FMDV genomes in the blood, (ii) the concentration of infectious virus in the blood, (iii) antibody levels, and (iv) interferon levels. Model parameters were estimated using maximum-likelihood methods. The likelihood surface was sampled using Markov chain Monte Carlo methods giving credible intervals for each of the model parameters. The model was able to capture the within-host dynamics well for 6 of the infections, with both the innate (type 1 interferon) and antibody responses playing key roles in determining the height and duration of peak levels of virus. There was considerable variation between virus dynamics in individual cattle which was only partly accounted for by inferred differences in the dose of virus received. A better understanding of the within-host dynamics also provides insights into the dynamics of infectiousness and the transmission of virus to new hosts.