A system for semiconductor wafer testing, a tangent probe card and a probe head assembly thereof. The system has a tangent probe card and a tester. Testing ends of the probe card are flat, hence the allowable alignment budget will always be more generous for the tangent probe card. The probes are held on the probe head assembly, and once the alignment is achieved accurately during manufacture, the alignment will remain stable throughout the whole life cycle. The probe has a greater CCC due to its larger cross section. The throughput of the tangent probes is higher than that of the conventional probe card since there is no need to move the pointed pin/structure. No pointed pin/structure needs to be repaired, and the flat bottom surface of the probe head assembly is easier to clean and maintain.