In this paper a segmentation algorithm of carotid arteries on computed tomography angiography (CTA) images is proposed. The algorithm is based on the threshold level set approach. In the basic version, the algorithm analyzes CTA slices beginning at the brachiocephalic trunk and going towards carotid arteries. Second variant of the algorithm performs segmentation in the opposite direction, which implies that the algorithm can follow branches e.g. subclavian arteries. The localization process of the initial contour, for threshold level set method, on the first slice is based on curvature anisotropic diffusion filter, the Gaussian filter and fast marching method. The article contains segmentation results for tested sets of method parameters. Experimental results show that optimal set of parameters ensuring that the threshold level set method performs segmentation of the entire subclavian arteries, does not exist.