A technique to obtain self-standing curved crystals has been developed. The method is based on a sandblasting process capable of producing an amorphized layer on the substrate. It is demonstrated that the amorphized layer behaves as a thin compressive film, causing the curvature of the substrate. This procedure permits the fabrication of homogeneously curved crystals in a fast and economical way. It is shown that a sandblasted crystal can be used as an X-ray optical element for astrophysical or medical applications. A sandblasted bent crystal can also be used as an optical element for steering charged particles in accelerator beamlines. Several samples were manufactured and bent using the sandblasting method at the Sensor and Semiconductor Laboratory of Ferrara, Italy. Their curvature was verified using interferometric profilometry, showing a deformation in agreement with the Stoney formalism. The curvature of the machined samples was also tested using γ-ray diffraction at the Institut Laue-Langevin (ILL), Grenoble, France. A good agreement with the dynamical theory of diffraction was observed. In particular, the experiment showed that the crystalline quality of the bulk was preserved. Moreover, the method allowed curved samples to be obtained free of any additional material. Finally, a crystalline undulator was produced using sandblasting and tested using γ-ray diffraction at the ILL. The crystal showed a precise undulating pattern, so it will be suitable for hard X-ray production