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In this study, a semi-analytical formulation based on the Scaled Boundary Finite Element Method (SBFEM) was proposed and used to obtain the solution for the characteristics of a two-dimensional dam-reservoir system with absorptive reservoir bottom in the frequency domain. For simplicity, the dam with arbitrary upstream faces was assumed to be rigid and was subjected to a horizontal ground acceleration, while the reservoir with absorptive bottom was assumed to be semi-infinite. The reservoir was divided into two sub-domains: a near-field sub-domain and a far-field sub-domain. The near-field sub-domain with arbitrary geometry was modelled by the Finite Element Method (FEM), while the effects of the far-field sub-domain which was assumed to be horizontal were described by a semi-analytical formation. The semi-analytical formulation involved the effect of absorptive reservoir bottom, as well as the radiation damping effect of a semi-infinite reservoir. A FEM/SBFEM coupling formulation was presented to solve dam-reservoir coupled problems. The accuracy and efficiency of the coupling formulation were demonstrated by computing some benchmark examples. Highly accurate results are produced even if the near-field sub-domain is very small.