A surface wave analysis method is developed for half-plane, periodic structures. The wave propagation is formulated by means of the Floquet transform. By virtue of the method, the dynamic problems in an infinite domain are reduced to that in a unit cell representing the periodicity. An impedance matrix describing the relation between displacements and tractions on the surface is derived from harmonic loading of infinite periodic domain by utilizing the inverse Floquet transform. The dispersion curves are obtained by exploring the eigenvalues of the impedance matrix. To cope with the singularity encountered in the inverse transform, the integration with respect to the wave number is extended to complex number. The feasibility of the developed method is evidenced by dispersion analysis of Rayleigh waves in a homogeneous half-plane. Though some difficulties are found in the analysis for periodic structures, pass and stop bands in lower frequencies can be captured successfully.