Clinical experience with extracorporeal shockwave lithotripsy (SWL) has demonstrated significant variations in stone fragility. To understand the physical mechanisms of the differences, we quantitatively determined shockwave-stone interaction under clinically relevant SWL conditions for six stone compositions: calcium oxalate monohydrate (COM), struvite (MAPH), calcium apatite (CA), uric acid (UA), brushite, and cystine. We also characterized the acoustic and mechanical properties of the stones using ultrasound and microindentation techniques. Our results show that renal calculi have distinctly different acoustic and mechanical properties. Higher wave speed, Young's modulus, and fracture toughness were measured from COM and cystine stones, whereas lower values of the corresponding properties were found in CA and MAPH, and the values for brushite and UA stones were in between. Computer modeling of shockwave propagation revealed that under the same shockwave intensity, larger deformation was induced in CA and MAPH stones than in COM and cystine stones. In addition, multiple reflected tensile waves were predicted for stones with concentric layer structure, indicating their susceptibility to shockwave fragmentation. These findings elucidate the mechanisms of the differences in stone fragility observed clinically. Their implications to SWL are discussed.