An anomalous material response has been observed under the action of applied compressive loads in fibrous SiC/Ti (both Ti-6242 and Ti-15-3 alloys) and the monolithic nickel-base alloy IN-718 in the aged condition. The observed behavior is an increase, rather than a decrease, in the instantaneous Young's modulus with increasing load. This increase is small, but can be significant in yield surface determination tests, where an equivalent offset strain on the order of 10 micron(1 x 10(exp -6) m/m) is being used. Stiffening has been quantified by calculating offset strains from the linear elastic loading line. The offset strains associated with stiffening during compressive loading are positive and of the same order as the target offset strains in yield surface determination tests. At this time we do not have a reasonable explanation for this response nor can we identify a deformation mechanism that might cause it. On the other hand, we are not convinced that it is an artifact of the experimental procedure because a number of issues have been identified and seemingly ruled out. In fact, stiffening appears to be temperature dependent, since it decreases as the temperature increases. Gil, Christopher M. and Lissenden, Cliff J. and Lerch, Bradley A. Glenn Research Center RTOP 523-21-13...