Inadequate sleep affects cognitive functioning, with often subtle and occasionally catastrophic personal and societal consequences. Unfortunately, this topic has received little attention in the cognitive modeling literature, despite the potential payoff. In this paper, we provide evidence regarding the impact of sleep deprivation on a particular component of cognitive performance, the ability to access and use declarative knowledge. Every 2h throughout an extended period of sleep deprivation, participants completed 50 trials of a serial addition/subtraction task requiring knowledge of single-digit arithmetic facts. Over the course of 88h awake, response times increased while accuracy declined. A computational model accounts for the degradation in performance through a reduction in the activation of declarative knowledge. This knowledge is required for successful completion of the serial addition/subtraction task, but access to the declarative knowledge is impaired as sleep deprivation increases and alertness declines. Importantly, the mechanism provides a generalizable quantitative account relevant to other tasks and contexts. It also provides a process-level understanding of how cognitive performance declines with increasing levels of sleep loss.