This paper introduces a method to evaluate the mechanical effects induced in the cross-section of an underground structure, constructed in a medium of great thickness, under earthquake ground motion. Damage observations after large earthquakes (e.g., Kobe, 1995) have shown the cross-sectional vulnerability of underground structures at shallow or great depth. Present earthquake-resistant design standards only suggest calculation methods for structures constructed in a soil laying over a rigid basement and cannot be applied to a structure constructed in a medium of great thickness, such as a tunnel, an underground hydrocarbon storage facility or a nuclear-waste disposal site. Thus, development of a systematic method to evaluate the seismic effects induced in the cross-section of a structure in an unbounded medium is of interest. The approach proposed here is conceptually similar to that used for earthquake response analysis of buildings: using a simple but realistic model of an underground linear structure (a 2D cavity with circular cross-section in an infinite, elastic, linear, homogeneous and isotropic medium) and real earthquake records, we propose a response spectrum more suitable, than the usual velocity or acceleration response spectrum, for analyzing the structural stability of underground construction during earthquakes: the Stress Response Spectrum (SRS), which is defined as the maximum value of the maximum shear stress at the cavity wall during the duration of ground motion. The SRS values are computed by using 21 earthquake motions (provided by the Japan Meteorological Agency) of magnitude higher than 4, which were recorded by the Japan Nuclear Cycle Research Institute (JNC) in a 315-meter deep gallery excavated in an a granodioritic rock mass at the Kamaishi Mine in Iwate, Japan. In light of the numerical analysis, the SRS appears to be a potential tool for the earthquake-response analysis of underground structures. The Stress Response Spectrum will provide engineers with the order of magnitude of mechanical effects in an underground structure for a given earthquake motion; conversely, for a given target SRS, may assist in producing a design earthquake more suitable for analysis of deep underground structures than those currently available.