The acoustic shear transmissibility and rigidity of saturated naphthenic hydrocarbon oils (NHO) with bridged carbon rings were determined by ultrasonic transmission analysis. In contrast to an established theory, we found that the NHO has superior transmissibility for transverse waves. It arises from appearance of quasi-elastic shear response under ultrasonic vibration, based on interlocking of the sterically hindered molecules with bridged rings. The shear and bulk moduli are of the order of 0.8-1.3 and 2.3-5.7 GPa at room temperature, respectively, indicating shear rigidity like solid polymers.