The human postural control system is difficult to quantify since it seems to be subject to both deterministic forces as well as stochastic effects. The attempt made in this paper is to study postural control under quiet stance on the one hand, and by engaging the brain through a fluency test, on the other. A Kistler electronic platform is the vehicle by way of which we gather observations in the form of center of pressure (COP) trajectories. From these two-dimensional trajectories we extract several measures that describe various features of the postural control system. Some of the measures are descriptive, while others incorporate physical forces that enter the process. From these measures we then build predictive models and apply them to a set of patients with Parkinson's disease (PD) and a set of normal control subjects to validate and calibrate them. We further use the measures built out of the center of pressure trajectories to test the significance of the fluency (cognitive-motor dual task) effect on the two groups. The fluency effect is found significant in the parkinsonian group as well as the normal controls. The clinical importance of these findings lies in the fact that the models may be used as a more objective assessment of postural control that may either replace or supplement the more subjective Unified Parkinson's Disease Rating Scale (UPDRS). The models may also be used as an assessment tool for the evaluation of patients subsequent to pharmacological and surgical treatment.