Abstract: In this paper, some kinds of singular integral equations of convolution type with reflection and translation shift are discussed and they are turned into Riemann boundary value problems with both discontinuous coefficients and reflection by using the Fourier transform. In spite of the classical method for solution, we are to give another method, therefore the general solution and condition of solvability are obtained in class {0}.

Key words: singular integral equation, convolution type, Riemann boundary value problem, reflection, translation shift