A series of uniaxial stress cycling experiments have been performed on dry Berea, Bandera, Boise, Ohio and Pecos sandstones, Carthage, Leuders and Glen Rose limestones and Austin Chalk in order to investigate effects of strain amplitude and stress on the static moduli. A servo-controlled rock mechanics test system has been used for the uniaxial stress cycling tests. Tests are conducted at a frequency of 10^-2 Hz frequency at different levels of strain amplitude and average stress. The static Young's moduli in sandstones shows a decreasing trend as strain amplitude is increased. Poisson's ratios increase with increasing strain. As the average stress is increased, sandstone samples yield higher Young's moduli whereas the opposite is observed in limestones. Data is presented to show that the dry static moduli are very sensitive to the strain amplitude and applied stress.