It is intuitive that a clamping element will grip better if the surface is provided with teeth which penetrate Into the surface of the clamped object. This paper is concerned with the problem of determining a quantitative comparison of the gripping ability of various penetrator shapes. It is presumed that the effects noted for a single penetrator will be applicable to an array of penetrators as on a serrated clamping element. Mathematical considerations show that a vertical penetrator load is held in equilibrium by the vertical components of the yield pressure which act on the penetrator surfaces. This is mathematically equivalent to the force given by the yield pressure acting over the area of the indentation projected on a plane normal to the direction of the load. This paper endeavors to show that the same concept will apply to forces applied transversely. Therefore the maximum possible transverse force which can be applied to a penetrator is theoretically equal to the product of the yield pressure of the Penetrated material and the area of tie penetrator face projected on a plane normal to the transverse force. Plasticity considerations show that the, yield pressure for a given material varies according to the penetrator shape. Strain hardening is also a factor in most materials. The influence of conventional friction is also shown to vary with the penetrator shape. In same cases vectorial addition of the frictional effect is required, but special cased permit algebraic addition. It is shown analytically that a friction reversal occurs at the surface of the penetrator as the transverse force roaches its maximum value. The result of the friction reversal is to lower the yield pressure Against the penetrator face. Experiments show that the foregoing theories are justified for the cases tested*