In this study, we present the cyclic degradation of the constrained modulus (M), determined using a standard triaxial device, while constraining lateral strains. These conditions replicate the soil response to propagating P-waves, which could be significant when analyzing nonlinear site response of the vertical ground motions. While vertical ground motions have been traditionally considered to be 2/3rd of the horizontal motions and to remain linear, studies show that the vertical component can exceed the horizontal one and can also display some nonlinear behavior. We performed a set of cyclic compressional tests, in which lateral deformation was constrained, such that no shear could develop. The tests were performed on coarse clean sand, under varying amplitudes of deviator stresses. The constrained modulus M was computed, and a degradation curve was constructed. We further study the effects of confining pressure, which shows to be a significant factor in similar shear-modulus (G) degradation curves. The results reveal that M decreases nonlinearly with the increase of axial strain and that M degradation curve shifts upward with the increase of confining stress, similar to that of the G degradation curve.