This paper describes a study of the stress-strain-pore water pressure behavior of Mexico City sediments subjected to one hundred sinusoidal stress-controlled cycles of loading. The influence of factors, such as, yielding stress, confining pressure, cyclic stress level and number of cycles was examined. Also the influence of cyclic loading on the post-cyclic undrained stress-strain characteristics of Mexico City sediments was studied. An isotropic consolidation test was conducted using a triaxial-cell method stress to define the yielding stress, σy. Then, two series of CU cyclic triaxial tests were conducted under different isotropic consolidation stress, to study the process of destructuration of the samples.