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This work presents an equivalent circuit to model the transmission/reflection of a plane wave that impinges obliquely on a periodic arrangement of metallic rectangular dipoles embedded between two dielectric slabs. The equivalent circuit takes advantage of the periodicity of the structure to reformulate the original problem as a certain equivalent waveguide scattering problem. Equivalent transmission lines are used to simulate the wave propagation whereas equivalent lumped circuit elements account for presence of the metallic patches. The obtaining of the circuit parameters is carried out via a systematic procedure, which provides a robust strategy that gives rise to surprisingly accurate results even for rather complex situations. The proposed equivalent circuit model simplifies considerably the original complex electromagnetic problem and provides a valuable physical insight into the parameters that are relevant in the phenomenon as well as an in-depth understanding of the operation principles of the periodic surface. Thus, the reported reduced-order model of the corresponding scattering problem can be a very convenient and helpful tool for the analysis and/or design of many practical devices.