It is known that Siegel's theorem on integral points is effective for Galois coverings of the projective line. In this paper we obtain a quantitative version of this result, giving an explicit upper bound for the heights of S-integral K-rational points in terms of the number field K, the set of places S and the defining equation of the curve. Our main tools are Baker's theory of linear forms in logarithms and the quantitative Eisenstein theorem due to Schmidt, Dwork and van der Poorten.