Two-dimensional elastodynamic problem for seismic response of unlined and lined tunnels located in a layered half-plane with free surface relief is solved. The computation tool uses the idea of the global matrix propagator method which allows derivation of a relation between the wave field quantities along different interfaces in the layered half- plane. The numerical realization of this idea is performed with the help of the sub-structured boundary element method (BEM) well suited when objects

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... with arbitrary geometry are considered. A relation between dis- placements and tractions along the free surface and arbitrary interface of the soil stratum is derived. It works for arbitrary geometry of the interfaces between soil layers. Finally, in the companion paper, numerical results are presented which show both a validation study of the pro- posed computational methodology and extensive numerical simulations demonstrating the influence of some important factors as type and characteristics of the incident wave, dynamic tunnels interaction, soil-tunnel interaction, free surface relief, type of the tunnel construction and mechanical properties of the layered half-plane on the complex seismic field near and far-away from the underground structures.