Stresses or deformations can be applied to a specimen, by at least one carrier having a number of flexible fingers extending therefrom, the fingers being securable to the specimen at spaced-apart locations, the carrier typically being attached to a motion-control and load measuring system. The fingers are relatively rigid in tension (or compression if desired) but flexible with respect to motions in other in-plane directions. They may or may not be flexible in out-of-plane directions. Commonly, there may be two carriers on opposite sides of the specimen for applying substantially uniaxial stress, or four carriers at 90 degrees to each other around the specimen for applying substantially biaxial stress, though any number of carriers may be used.