During clinical procedures, the lithotripter shock wave (LSW) that is incident on the stone and resultant stress field is often asymmetric due to the respiratory motion of the patient. The variations of the LSW-stone interaction and associated fracture pattern were investigated by photoelastic imaging, phantom experiments, and three-dimensional fluid-solid interaction modeling at different lateral locations in a lithotripter field. In contrast to a T-shaped fracture pattern often observed in the posterior region of the disk-shaped stone under symmetric loading, the fracture pattern gradually transitioned to a tilted L-shape under asymmetric loading conditions. Moreover, the model simulations revealed the generation of surface acoustic waves (SAWs), i.e., a leaky Rayleigh wave on the anterior boundary and Scholte wave on the posterior boundary of the stone. The propagation of SAWs on the stone boundary is accompanied by a progressive transition of the LSW reflection pattern from regular to von Neumann and to weak von Neumann reflection near the glancing incidence and, concomitantly, the development and growth of a Mach stem, swirling around the stone boundary. The maximum tensile stress and stress integral were produced by SAWs on the stone boundary under asymmetric loading conditions, which drove the initiation and extension of surface cracks into the bulk of the stone that is confirmed by micro-computed tomography analysis.