Terahertz time-domain spectroscopy (THz TDS) is a well-known tool for material analysis in the terahertz frequency band. One crucial system component in every time-domain spectrometer is the delay line which is necessary to accomplish the sampling of the electric field over time. Despite the fact that most of the uncertainty sources in TDS have been discussed, the delay line uncertainty has not been considered in detail. We model the impact of delay line uncertainty on the acquired THz TDS data. Interferometric measurements of the delay line precision and THz time-domain data are used to validate the theoretical model.