Potential energy surfaces for the electronic states of the HCCS radical correlating at linear nuclear arrangement with the X (2)Pi state are calculated by means of an extensive ab initio approach. Particular attention is paid to calculating accurate three-dimensional potential surfaces involving variations of two bending and torsional coordinates, which play the central role in vibronic interactions (Renner-Teller effect), determining the structure of spectra of this radical. In the second part of this paper we use these potential surfaces and the ab initio computed spin-orbit coupling constant to calculate vibronic spectra of HCCS and DCCS in the framework of a theoretical model developed in our laboratory. The results of the present study are in excellent agreement with those derived by Tang and Saito [J. Chem. Phys. 105, 8020 (1996)] and thus strongly support the interpretation of their experimental findings.