The instantaneous relationship between arterial blood pressure (BP) and cerebral blood flow velocity (CBFV), measured with Doppler ultrasound in the anterior cerebral artery, is represented by a vascular waterfall model comprising vascular resistance, compliance, and critical closing pressure. One min recordings obtained from 61 low birth weight newborns were fitted to the model using a least-squares procedures with correction for the time delay between the BP and CBFV signals. A sensitivity analysis was performed to study the effects of low-pass filtering (LPF), cutoff frequency, and noise on the estimated parameters of the model. Results indicate excellent fitting of the model (F-test, p < 0.0001) when the BP and CBFV signals are LPF at 7.5 Hz. Reconstructed CBFV waveforms using the BP signal and the model parameters have a mean correlation coefficient of 0.94 with the measured flow velocity tracing (N = 232 epochs). The model developed can be useful for interpreting clinical findings and as a framework for research into cerebral autoregulation.