Cerebral autoregulation refers to the physiological process that maintains stable cerebral blood flow (CBF) during changes in arterial blood pressure (ABP). In this study, we propose a simple, nonlinear quantitative model with only four parameters that can predict CBF velocity as a function of ABP. The model was motivated by the viscoelastic-like behavior observed in the data collected during postural change from sitting to standing. Qualitative testing of the model involved analysis of dynamic responses to step-changes in pressure both within and outside the autoregulatory range, while quantitative testing was used to show that the model can fit dynamics observed in data measured from a healthy young and a healthy elderly subject. The latter involved analysis of structural and practical identifiability, sensitivity analysis, and parameter estimation. Results showed that the model is able to reproduce observed overshoot and adaptation and predict the different responses in the healthy young and the healthy elderly subject. For the healthy young subject, the overshoot was significantly more pronounced than for the elderly subject, but the recovery time was longer for the young subject. These differences resulted in different parameter values estimated using the two datasets.