Understanding of the static internal stress in supported thin layers can be aided by the use of dynamic mechanical analysis, with emphasis on internal friction measurements for the detection of defects susceptible to stress-induced ordering. In addition to the bending-bilayer and vibrating-reed methods used for separate measurements of internal stress and internal friction, a new vibrating-membrane method is described that enables both quantities to be measured concurrently on the same sample. Structural relaxation, solute sorption, orientational ordering, and surface reaction are identified as four general phenomena affecting the internal stress, and experimental results are given for each of these categories. The bending-bilayer method has been used to observe stress changes associated with structural relaxation in amorphous SiO films, and with the sorption and orientational ordering of oxygen in Nb films. The vibrating-membrane method has been used to study stress changes in boron-doped Si membranes, resulting from either hydrogen sorption or high-temperature oxidation. Hydrogen sorption leads to the appearance of a new internal friction peak located near 130 K, which is governed by an activation energy of 0.23 eV.