Tunable control of X-ray waves remains an open challenge of critical importance for applications in high-resolution X-ray spectroscopy, medical imaging, and radiation therapy. Unlike in the X-ray regime, control over light waves in the visible and IR regimes is ubiquitous in a vast range of applications, and typically relies on widely available optical components. However, analogous optical elements for X-rays are usually inefficient and challenging to fabricate. Here, we propose a method for shaping X-ray waves directly at the source, using the interaction of free electrons with crystalline materials. Specifically, by inducing strain on van der Waals materials, we control their interaction with free electrons in a manner that tunes the emissions of the X-rays and forms caustic X-ray beams. The development of wave-shaping concepts like caustics generation in the X-ray spectral range could benefit from achievements in this field in the optical range and may help bypass the noted limits of current X-ray optics technology. Looking forward, shaping the interference of X-rays at the atomic scale could enable further developments in high-resolution X-ray science.