In this paper, we discuss the Riemann boundary value problems for the analytic functions with period (Formula presented.) (Formula presented.) in the situation where the solution can be unbounded at (Formula presented.). When the jump curve is a closed contour, by using the tangent transformation (Formula presented.), we transform the singularities (Formula presented.) on the z plane to the singularities (Formula presented.) on the ζ plane. When the jump curve is the real axis, by using the transformation (Formula presented.), we transform the singularities (Formula presented.) on the z plane to the singularities 0 and ∞ on the ω plane. Thus, the original periodic Riemann boundary value problems are reduced to the classical Riemann boundary value problems whose solutions and the corresponding solvability conditions are well known.