The　tuned　mass　damper　(TMD)　is　widely　used　for　vibration　mitigation,　especially　in　high-rise　buildings　where　significant　soil-structure　interaction　(SSI)　effects　are　usually　involved.　This　creates　a　need　to　consider　SSI　effects　in　TMD　design.　In　this　work,　a　novel　design　framework　for　TMD　systems　with　SSI　effects　is　proposed.　For　response　evaluations,　structure-TMD　systems　are　modeled　as　a　two-degrees-of-freedom　(2DOF)　system,　standing　on　a　rigid　foundation　and　subject　to　out-of-plane　SH　seismic　wave　inputs　in　a　homogeneous　half-space.　Closed-form　analytical　solutions　of　its　displacement　and　acceleration　responses　are　derived,　and　the　H-2-norm　of　the　system　transfer　function　is　introduced　to　quantify　the　performances　of　TMDs.　The　TMD　design　problem　is　then　formulated　and　solved　by　optimizing　the　performances.　Considering　that　aspects　other　than　response　mitigation,　e.g.,　strokes,　damper　device　costs,　etc.,　may　be　critical　to　TMD　damping　ratios,　a　design　framework　is　developed　by　firstly　making　an　informed　selection　on　TMD　damping　ratios,　and　subsequently　tuning　TMD　frequency　ratios　through　calibrated　formulae.　In　addition,　TMD　strokes　versus　TMD　damping　ratios　are　investigated　to　facilitate　the　determination　of　TMD　damping　ratios.　A　case　study　based　on　a　real-existing　building　system　is　carried　out　to　illustrate　the　application　of　the　proposed　design　framework.　The　framework　has　proven　to　be　highly　efficient　and　effective　and　suitable　to　for　use　in　practical　engineering.