Instabilities occur frequently in ocean-bottom sediments where the deposition is faster than the consolidation of the material. Cyclic loading of waves contribute to the existing pore pressures within the sediment reducing the effective stresses. The sediment can lose strength and stability and flow in gullies of depth up to 30 m, on slopes less than 0.5 deg. One theory and some related experiments indicate that, depending on the depositional conditions and state of stress, the failure mechanism for such soft saturated marine clays may not necessarily require large straining of the material. Laboratory determination of low-strain shear behavior or shear modulus of soft marine clays can be complicated if high-frequency dynamic testing methods are utilized. Cyclic loading can promote fast degradation of moduli for these soils even at low strain amplitudes. A monotonic torsional shear device, namely a triaxial vane device, was equipped with a computer-aided data acquisition system to detect low-strain shear deformations under quasi-static loading conditions. The average range of electronically measured strain range was 10−4 to 1 percent, which was compatible with that of a high-frequency, low-strain dynamic testing method, namely, resonant column. Comparison of the dynamic and static moduli reduction curves of artificially prepared soft kaolinite specimens demonstrated the cyclic degradation effects on such clays. The relatively continuous, high-resolution low-strain static data indicated further gain in understanding of low-strain nonlinearity and yielding behavior of soft marine clays.