In this paper, we investigate the exact method of searching an axis of binary image symmetry, based on brute-force search among all potential symmetry axes. As a measure of symmetry, we use the set-theoretic Jaccard similarity applied to two subsets of pixels of the image which is divided by some axis. Brute-force search algorithm definitely finds the axis of approximate symmetry which could be considered as ground-truth, but it requires quite a lot of time to process each image. As a first step of our contribution we develop the parallel version of the brute-force algorithm. It allows us to process large image databases and obtain the desired axis of approximate symmetry for each shape in database. Experimental studies implemented on “Butterflies” and “Flavia” datasets have shown that the proposed algorithm takes several minutes per image to find a symmetry axis. However, in case of real-world applications we need computational efficiency which allows solving the task of symmetry axis search in real or quasi-real time. So, for the task of fast shape symmetry calculation on the common multicore PC we elaborated another parallel program, which based on the procedure suggested before in (Fedotova, 2016). That method takes as an initial axis the axis obtained by superfast comparison of two skeleton primitive sub-chains. This process takes about 0.5 sec on the common PC, it is considerably faster than any of the optimized brute-force methods including ones implemented in supercomputer. In our experiments for 70 percent of cases the found axis coincides with the ground-truth one absolutely, and for the rest of cases it is very close to the ground-truth.