Rumination involves repetitive dwelling on negative thoughts, emotions and memories and is a risk factor for depression. Cognitive theories suggest that rumination stems from heightened automatic, emotional stimuli-driven (i.e., “bottom-up”) and/or deficits in effortful, goal-directed (i.e., “top-down”) processes. It remains unclear whether rumination arises from bottom-up processes impacting top-down inhibitory control, or from impaired inhibition alone. We used both experimental and computational approaches to address this. Participants (N=151) first completed self-report measures of trait rumination, followed by the standard and emotional Stroop tasks, before and after a rumination induction. Brooding, a maladaptive component of rumination, was associated with slower reaction times for both tasks. A rumination induction, expected to heighten bottom-up emotional salience, increased Stroop interference in proportion to brooding severity. To study underlying computational mechanisms, we adapted an existing parallel distributed processing model of the Stroop task to include mechanisms for emotional cue processing, and subsequently numerically fit the model parameters to individual participant Stroop data. Brooding was positively associated with bottom-up weights and steeper neural activation curves in the task control layer, representing a greater sensitivity to emotional cues and changes in task demands. Higher brooding also predicted faster temporal integration (i.e., activity decay) of top-down control signals, and slower temporal integration (i.e., activity persistence) of emotional cues. We therefore propose that a greater sensitivity to changes in task demands and bottom-up emotional cues, along with a diminished capacity to sustain goal-relevant control signals, underlie inhibitory control deficits in trait rumination.