Silver noble metal nanoparticles that are <10 nm often possess multiply twinned grains allowing them to adopt shapes and atomic structures not observed in bulk materials. The properties exhibited by particles with multiply twinned polycrystalline structures are often far different from those of single-crystalline particles and from the bulk. I will present experimental evidence that silver nanoparticles <10 nm undergo a reversible structural transformation under hydrostatic pressures up to 10 GPa. Results for nanoparticles in the intermediate size range of 5 to 10 nm suggest a reversible linear pressure-dependent rhombohedral distortion which has not been previously observed in bulk silver. I propose a mechanism for this transitiion that considers the bond-length distribution in idealized multiply twinned icosahedral particles. Results for nanoparticles of 3.9 nm suggest a reversible linear pressure-dependent orthorhombic distortion. This distortion is interpreted in the context of idealized decahedral particles. In addition, given these size-dependent measurements of silver nanoparticle compression with pressure, we have constructed a pressure calibration curve. Encapsulating these silver nanoparticles in hollow metal oxide nanospheres then allows us to measure the pressure inside a nanoshell using x-ray diffraction. We demonstrate the measurement of pressure gradients across nanoshells and show that these nanoshells have maximum resolved shear strengths on the order of 500 MPa to IGPa.