This study aims to identify the effect of stiffness on renal artery Doppler sonograms by using a curve fitting approach. The study includes 20 patients with suspected renovascular hypertension. Each patient underwent recordings during renal artery examinations before and after administration of Captopril 25 mg (Kapril tablet, MN Pharmaceuticals, Istanbul, Turkey). Doppler signals were analyzed with short time Fourier transformation, followed by curve fitting to sonograms using Savitzky-Golay method. Doppler parameters obtained from pre- and post-Captopril curve-fitted sonograms were statistically compared with "Paired-Samples t-Test". Captopril administration resulted in a significant decrease in the mean frequency and a significant increase in Pulsatility Index of the periods. No significant difference was detected between maximum systolic and minimum diastolic frequencies, Resistivity Index, and the Acceleration Index. The computational approach in this study appears to be promising.