Shale gas is becoming an increasingly important energy source worldwide. The geomechanical properties of shale rocks can have a major impact on the efficiency of shale gas exploration. This paper studies the mineralogical and mechanical characteristics of a typical gas shale in Ohio, USA. A scanning electron microscope (SEM) with Energy Dispersive X-ray (EDX) analyses was employed to measure the microstructure and material composition of the shale rock. The anisotropic behaviors of shale rock, including compressive and tensile strength, were experimentally measured. The effects of anisotropy on the observed strength behaviors and failure patterns were discussed. The characteristics of shale rock are also studied by non-destructive wave speed measurements. The shale demonstrated strong anisotropic behaviors with the tensile strength perpendicular to the bedding plane around 300-360 times of that parallel to the bedding plane. Results of ultrasonic testing indicated that both compression and shear wave velocities show strong anisotropic patterns. The compression wave speed was smallest in the direction perpendicular to the bedding plane, while the shear wave speed was smallest in the direction parallel to the bedding plane. The ratio of wave speed anisotropy is around 1.3-1.4 times for compression wave. The ratio of wave speed anisotropy is more diverse for shear wave.