Solder interconnection in electronic packaging is the weakest link, thus driving the reliability of electronic modules and systems. Improving interconnection integrity in safety-critical applications is vital in enhancing application reliability. This investigation qualifies the random vibration response of five essential solder compositions in ball grid array (BGA) solder joints used in safety-critical applications. The solder compositions are eutectic Sn63Pb37 and SnAgCu (SAC) 305, 387, 396, and 405. Computer-aided engineering (CAE) employing ANSYS finite element analysis and SolidWorks software is implemented in this investigation. The solder Sn63Pb37 deformed least at 0.43 µm, followed by SAC396 at 0.58 µm, while SAC405 deformed highest at 0.88 µm. Further analysis demonstrates that the possession of a higher elastic modulus and mass density culminates in lower solder joint deformation. Stress is concentrated at the periphery of the solder joints in contact with a printed circuit board (PCB). The SAC396 solder accumulates the lowest stress of 14.1 MPa, followed by SAC405 at 17.9 MPa, while eutectic Sn63Pb37 accrues the highest at 34.6 MPa. Similarly, strain concentration is found at the interface between the solder joint and copper pad on a PCB. SAC405 acquires the lowest elastic strain magnitude of 0.0011 mm/mm, while SAC305 records the highest strain of 0.002 mm/mm. These results demonstrate that SAC405 solder has maximum and SAC387 solder has minimum fatigue lives.