Mental calculation is an important everyday skill involving access to well-learned procedures, problem solving, and working memory. Although there is an active literature on acquiring concepts and procedures for mental arithmetic, relatively little is known about the role of working memory in this task. This paper reports two experiments in which dual-task methodology is used to study the role of components of working memory in mental addition. In Experiment 1, mental addition of auditorily presented two-digit numbers was significantly disrupted by concurrent random letter generation and, to a lesser extent, by concurrent articulatory suppression, but was unimpaired by concurrent hand movement or by presentation of irrelevant pictures. Although the number of errors increased with two of the dual tasks, the incorrect responses tended to be quite close to the correct answer. In Experiment 2, the numbers for addition were presented visually. Here again, random generation produced the largest disruption of mental arithmetic performance, while a smaller amount of disruption was observed for articulatory suppression, hand movement, and unattended auditorily presented two-digit numbers. The overall levels of performance were better and the absolute size of the disruptive effects shown with visual presentation was very small compared with those found for auditory presentation. This pattern of results is consistent with a role for a central executive component of working memory in performing the calculations required for mental addition and in producing approximately correct answers. Visuospatial resources in working memory may also be involved in approximations. The data support the view that the subvocal rehearsal component of working memory provides a means of maintaining accuracy in mental arithmetic, and this matches a similar conclusion derived from previous work on counting. The general implications for the role of working memory in arithmetic problem solving will be discussed.