The nature of interference in working memory has been a subject of discussion for decades. It has previously been argued that irrelevant stimuli can interfere with working memory by being encoded into memory. Previous findings have suggested that irrelevant sensory activity can interfere with the storage of information in tactile working memory. More recently, it has been suggested that this type of interference may operate through the overwriting of stored information by interfering sensory stimuli, even when participants are instructed to ignore such stimuli. Such a mechanism of interference is consistent with previous theoretical proposals. In the present study, we use a computational diffusion model to demonstrate that previous empirical findings are best explained by the encoding of irrelevant sensory information and subsequent interference.