Nanometer-scale-thick films of metals and semiconductor heterostructures are used increasingly in modern technologies, from microelectronics to various areas of nanofabrication. Processing of such ultrathin-film materials generates structural defects, including voids and cracks, and may induce structural transformations. Furthermore, the mechanical behavior of these small-volume structures is very different from that of bulk materials. Improvement of the reliability, functionality, and performance of nano-scale devices requires a fundamental understanding of the atomistic mechanisms that govern the thin-film response to mechanical loading in order to establish links between the films' structural evolution and their mechanical behavior. Toward this end, a significant part of this study is focused on the analysis of atomic-scale mechanisms of plastic deformation in freestanding, ultrathin films of face-centered cubic (fcc) copper (Cu) that are subjected to biaxial tensile strain. The analysis is based on large-scale molecular-dynamics simulations. Elementary mechanisms of dislocation nucleation are studied and several problems involving the structural evolution of the thin films due to the glide of and interactions between dislocations are addressed. These problems include void nucleation, martensitic transformation, and the role of stacking faults in facilitating dislocation depletion in ultrathin films and other small-volume structures of fcc metals. Void nucleation is analyzed as a mechanism of strain relaxation in Cu thin films. The glide of multiple dislocations causes shearing of atomic planes and leads to formation of surface pits, while vacancies are generated due to the glide motion of jogged dislocations. Coalescence of vacancy clusters with surface pits leads to formation of voids. In addition, the phase transformation of fcc Cu films to hexagonal-close packed (hcp) ones is studied. The resulting martensite phase nucleates at the film's free surface and grows into the bulk of the film due to dislocation glide. The role of surface orientation in the strain relaxation of these strained thin films under biaxial tension is discussed and the stability of the fcc crystalline phase is analyzed. Finally, the mechanical response during dynamic tensile straining of pre-treated fcc metallic thin films with varying propensities for formation of stacking faults is analyzed. Interactions between dislocations and stacking faults play a significant role in the cross-slip and eventual annihilation of dislocations in films of fcc metals with low-to-medium values of the stable-to-unstable stacking-fault energy ratio, γs/γu. Stacking-fault-mediated mechanisms of dislocation depletion in these ultrathin fcc metallic films are identified and analyzed. Additionally, a theoretical analysis for the kinetics of strain relaxation in Si 1-x Ge x (0 ≤ x ≤ 1) thin films grown epitaxially on Si(001) substrates is conducted. The analysis is based on a properly parameterized dislocation mean-field theoretical model that describes plastic-deformation dynamics due to threading dislocation propagation; the analysis addresses strain relaxation kinetics during both epitaxial growth and thermal annealing, including post-implantation annealing. The theoretical predictions for strain relaxation as a function of film thickness in Si 0.80 Ge 0.20 /Si(001) samples annealed after growth, either unimplanted or after He + implantation, are in excellent agreement with reported experimental measurements.