Tortuosity of eye fundus blood vessels is one of parameters that describe state of the blood vessels. It can be detected from fundus images. The increase in vessel tortuosity was observed in eyes of patients with advanced background diabetic retinopathy, papilloedema, arterial hypertension, even in some completely healthy eyes (in this case tortuosity does not change in time). Thus the feature of the line – tortousity – could be used as the diagnostic feature in medical applications. Unfortunately, completely reliable definition and numerical estimation of tortuosity of line (blood vessel) does not exist, although there were some more or less successful attempts to define it. This work presents a new way to estimate the tortuosity using the integral of square derivative of curvature. It is compared with the existing methods both theoretically and experimentally. Three types of lines have been used for experimental comparison: theoretical models of retinal vessels (straight line, parabola, sinusoid and their combinations), lines extracted from real fundus images and lines extracted from optometric scale for retinal vessel evaluation. To ease the extraction of the lines from these images a new version of one of the methods for vessel tracking has been created and implemented.