Stress plays an important role in materials science, and applying stress is a useful and effective method of modulating the properties of materials. In this thesis, we investigate the effects of stress on the properties of materials using first-principles calculations based on the density functional theory. The research covers a broad range of materials systems, from three-dimensional bulk materials to low-dimensional nanostructured materials. In three-dimensional systems, hydrostatic stress fields can be considered as pressure, which can be routinely obtained from man-made high-pressure devices. At high pressures, most materials undergo phase transitions and exhibit novel properties, such as metallization and superconductivity. We study the high-pressure behaviors of GeH4 and alkaline earth hydrides. GeH4 undergoes a structural transformation from its low-pressure P21/c phase to a high-pressure Cmmm phase at about 15 GPa where insulator-metal transition occurs, followed by two other metallic phases with P21/m and C2/c symmetries up to 200 GPa. Our results indicate that the metallization of GeH4 can be realized through a band overlap within the material itself. Perturbative linear response calculations for Cmmm GeH4 at 20 GPa predict a strong electron-phonon interaction, and the resulting superconducting critical temperature is about 40 K. We investigate systematically the structural and electronic properties of alkaline earth hydrides under pressure, and emphasize the pressure-induced metallization of alkaline earth hydrides. While BeH2 and MgH2 have different semi-metallic phases, CaH2, SrH2, and BaH2 share the same metallic phase (P6/mmm). The metallization pressure shows an attractive decrease with the increment of alkaline earth metal radius and band gap of alkaline earth hydrides at ambient pressure. BaH2 has the lowest metallization pressure; hence its phase transition mechanism and vibrational properties under pressure are studied. Our results are consistent with current experimental data, and the obtained trend has significant implications for designing and engineering metallic hydrides for energy applications. For low-dimensional nanostructured systems, we focused on the effects of stress on Si sheets and Ge nanowires. For a (100) Si sheet, asymmetrical strain causes a direct-to-indirect band gap transition, whereas symmetrical strain keeps its direct band gap characteristics unchanged. Under asymmetrical strain along the <100> direction, the direct band gap of the (110) Si sheet exhibits unique characteristics, with the direct band gap varying linearly with the change in strain. Similar band gap variation is observed for (110) Si sheets applied with symmetrical and asymmetrical <110> strains. The various strain dependences are related to the modifications of the local density of states. Our results could be used to guide the strain engineering of the electronic properties of low-dimensional silicon materials. We investigate strain effects on the electronic properties of germanium nanowires (GeNWs) along the <112> direction. The <112> GeNWs possess direct band gaps when the cross-section aspect ratio of (111) to (110) facets is larger than 1. The strain does not change the direct band gap characteristics; however, compressive (tensile) strain tends to increase (decrease) the band gap. The variation in band gaps originates from the different strain dependences of valence bands and conduction bands. Our results suggest that both strain and size can be used to tune the band structures of GeNWs, which may help in designing future nanoelectronic devices.