An integral equation associated with a mixed distribution of source and normal doublet on the wetted surface of a two dimensional body has been presented for calculating the hydrodynamic coefficients of an oscillating cylinder in steady horizontal translation on the free surface. This equation contains two dimensional equivalent of the line integral for a three dimensional surface-piercing body. It also contains an integral relation which eliminate the occurrence of irrelevant solution. The resulting overdetermined linear system is solved by the method of Householder. Hydrodynamic coefficients of a half immersed circular cylinder have been calculated for various Froude numbers up to 0.35. The present numerical results fur a very small Froude number agree well with those for zero Froude number. It seems that the present method yields reasonable numerical results for all frequencies without restriction on the magnitude of Froude number in the context of linear wave theory.