Abnormal excitation of the heart can cause cardiac arrhythmias, which may result in cardiac arrest and sudden cardiac death. Currently, the most efficient way to stop lethal cardiac arrhythmias is high-voltage defibrillation. This method is extremely effective. However, it has serious disadvantages, as it is painful and can damage the heart. In this paper, we studied in-silico process of overdrive pacing of arrhythmia sources, which in some cases can also stop cardiac arrhythmias and does not require the application of high voltages. We investigated this process in the Luo–Rudy ionic model for cardiac cells and in case of circular anisotropy of cardiac tissue. We showed that we could efficiently remove the arrhythmia sources in the form of rotating spiral waves in such a system in a certain parameter range. However, anisotropy by itself can cause additional dynamics of the spiral waves: drift and break up. We studied manifestations of these effects and discussed their possible effects on the overdrive pacing. This paper is an extended version of the paper [1] which was submitted to the ICCS 2018 conference proceedings.