Hypervelocity impact tests were conducted on gas-filled cylindrical stainless steel thin wall pressure vessels. Without shield the vessels can be penetrated by even V1mm 2A12 aluminum projectiles. With shield the damage of vessels was slightly affected by interior pressure of 0~6 MPa, strongly affected by interior pressure 8~10 MPa, even burst at 10 MPa. Ballistic limit curve under experimental condition was obtained. The relation between failure and pressure of vessels was analyzed through conservative fracture mechanics approach. Then a critical P-a curve of pressure vessels was constructed which described relation between inner pressure and crack size. It was considered that crack of the pressure vessels was intensely growing during the process of burst, and crack of pressure vessels suffering to hypervelocity impact was governed by the combination of inner pressure P and additional shock pressure DeltaP', which was calculated as 0.47MPa. Based on above result a predictive critical P-a curve was got to forecast if pressure vessels would burst or not.