The multimode method of Cheng and Mitchell <1981> is used to study the attenuation properties of the crust throughout the Barents shelf. The sensitivity of the spectra to various source factors and to propagation factors which might characterize a shelf region are thoroughly studied. For plane-layered models, the method is very sensitive to Qβ in the upper crust and to Qβ of sedimentary layers if those layers are thick and highly attenuating. It is far less sensitive to Qβ in the lower crust and to Qα. The spectra, for shallow strike slip earthquakes, are very insensitive to changes in strike, slip, and dip angles of the fault throughout the entire period range of interest but are very sensitive to variations in focal depth except in the long-period range of the fundamental mode and the short-period range of the higher modes. The fundamental mode, but not the higher mode, spectra for one path across the Barents shelf are, apparently, distorted at short periods by lateral heterogeneities along the travel path. Simple two-layer, trial-and-error inversions yield a model of the Barents shelf with an upper crustal Qβ value of about 80. Three-layer inversions with a sedimentary layer, however, yield an upper crustal Qβ of about 250, if the sediments are 1 km thick and are characterized by Qβ values of 40. Shear velocity models for the Barents shelf show variations between about 3.0 and 3.6 km/s in the upper crust along different paths. The lower crust shows smaller regional differences, but velocities vary between 3.5 and 4.0 km/s through the depth range 25--35 km. The variation of shear velocities in the upper mantle may correlate with those of the upper crust and vary regionally between about 4.3 and 4.8 km/s.