Perennially frozen soils, or permafrost, exist extensively on the Arctic Coastal Plain of Alaska and can reach up to 600 m deep. This paper describes the cryostructure of permafrost cores obtained from a deep borehole in this area, presents the shear wave velocities measured in different directions by the bender element method, exhibits the small-strain shear moduli of clay, silt and sand permafrost specimens from −10 °C to 20 °C, and discusses the anisotropy in the small-strain shear modulus of permafrost in both frozen and thawed states. It was found that the specimen site is covered by a few meters of syngenetic permafrost with massive wedge ice, below which is a deep epigenetic permafrost with numerous visible ice lenses primarily located in the top 120 m, oriented in horizontal or subhorizontal directions. The shear modulus ratio found for thawed clay permafrost falls in the higher end of those reported for natural or reconstituted clays, while the ratio for thawed sand permafrost is clearly higher than those previously reported. The anisotropy in the small-strain shear modulus was found to be strongly temperature dependent. The temperature dependency of anisotropy can be attributed to volumetric expansion, occurring during the freezing of pore water followed by the thawing of pore ice that, respectively, disrupts then allows the recovery of the preferential alignment of soil particles, or fabric, formed during geological sedimentation processes. In addition, deep permafrost cores with shear stiffness comparable to hard rock exhibit a very low stiffness ratio Ghh/Gvh, likely due to the in situ geostatic stress-induced anisotropy in pore ice crystals.