Despite the well-defined behavioral criteria for posttraumatic stress disorder (PTSD), clinical care is complicated by the heterogeneity of biological factors underlying impairment. Eye movement tasks provide an opportunity to assess the relationships between aberrant neurobiological function and non-volitional performance metrics that are not dependent on self-report. A recent study using an emotional variant of the antisaccade task demonstrated attentional control biases that interfered with task performance in Veterans with PTSD. Here we present a neuroanatomically-inspired computational model based on gated attractor networks that is designed to replicate oculomotor behavior on an affective anti-saccade task. The model includes the putative neural circuitry underlying fear response (amygdala) and top-down inhibitory control (prefrontal cortex), and is capable of generating testable predictions about the causal implications of changes in this circuitry on task performance and neural activation associated with PTSD. Calibrating the model with the results of behavioral and neuroimaging studies on patient populations yields a pattern of connectivity changes characterized by increased amygdala sensitivity and reduced top-down prefrontal control that is consistent with the fear conditioning model of PTSD. In addition, the model makes experimentally verifiable predictions about the consequences of increased prefrontal connectivity associated with cognitive reappraisal training.