In order to maintain a continuous power suppply, nowadays relays in transmission systems are required to be able to deal with complicated faults involving non-conventional connections, which poses a challenge to the short circuit analysis performed for the data settings of the relay. The traditional sequence domain method has congenital defects to treat such cases, which leads to a trend of using the actual phase domain method in fault calculation. Although the calculation speed of the phase domain method is not so fast and is memory consumable, it perfomrs well when handling complicated faults. Today more and more commercial software involves phase domain calculation in their short circuit analysis to treat complicated cases. With the advanced development of computers, there is a possibility to totally get rid of the sequence method. In this thesis, a short circuit analysis method based on phase domain is developed. After the three sequence admittance matrices of the system are built, all the data are transformed into phase domain to get the phase domain admittance matrix. The following fault calculations are performed purely in phase domain. The test results of different types of faults in 3 bus, 14 bus, and 30 bus transmission systems are presented and compared with the results of a commercial fault analysis software. The validation of this program is also presented.