In two experiments, young and older adults solved arithmetic chain tasks with single-digit operands, with or without a concurrent memory load of three or six digits. Variables in the arithmetic tasks had to be replaced by digits from the screen or from the memory set. A task-irrelevant concurrent load impaired neither speed nor accuracy of arithmetic in younger adults. In Experiment 2, this was also true for older adults. A large decrease in arithmetic performance was observed, however, when variables in the arithmetic task had to be substituted by digits from the memory list. Older adults had specific problems with this condition in Experiment 1, where the substitution involved two successive steps, but not in Experiment 2, where the substitution from memory could be done in a single step. The results are difficult to reconcile with models assuming a common resource for storage and processing. Rather, they are compatible with the hypothesis that a concurrent memory load interferes with a processing task only during the points of access to working memory. Further, even though access to working memory was found to be the critical source of concurrent-load interference, it was found to be insensitive to the effects of adult aging.