I would like to agree with TGS4 and dhengr and then up the ante. DO NOT CONSIDER DESIGNING THIS PRODUCT.
That being said, the design of this test vessel is going to be the least of your problems and the least expense. I work in a facility that routinely tests our products to 20,000 psi.
The testing is done in a bunker. The pressure vessel is underground, in this bunker, deep enough to be surrounded by thousands of tons of dirt. The access to the bunker is through a vertical shaft and the shaft has an access room at the surface made of concrete walls and a concrete ceiling. The walls are thick. Really thick. The roof (directly above the shaft) is even thicker - 3 feet of reinforced concrete.
The reinforced concrete doors are operated by enormous gearmotors and electronically controlled and monitored. Ridiculously meticulous security procedures and equipment has been implemented, including motion detectors inside the room to help ensure no person is inside the surface building when testing is performed.
That being said, I would now like to give you the good news. You do not have to design your vessel. You can rent it or buy it. Call around in Houston, TX, Edmonton, AB or Houma, LA to oilfield service equipment manufacturers and look for an API 6A riser spool used in well servicing operations. You can easily find a 13.625" ID riser spool flanged on each end and get it in most any length you need. These spools are offered in standard pressure ratings of 2ksi, 3ksi, 5ksi, 10ksi, 15ksi and 20ksi. I don't know what you're testing, but hopefully whatever it is, it will fit inside of a 13.625 ID. If it's smaller, you can find smaller-bore equipment. You can also readily find the normal accessories that you would need to assemble your test apparatus. Flanges, blind flanges, metal-to-metal seals for properly sealing these items, reducers, adapters, etc. And for connecting these items between your pressure vessel and your pump and instrumentation, Autoclave makes every manner of tubing, fitting and connector capable of up to 60ksi pressures.
After you have built your bunker and containment room, you still have huge tasks ahead of you including determining a way of removing all gases from your vessel, use only liquids that have been degassed for the testing, implement a testing procedure for the vessel itself - standard in my industry is full magnetic particle and ultrasonic or x-ray testing every three months of service (check with your manufacturer), find a big enough tire pump and then hide behind a D9 Caterpillar.
Again, I will make the statement as strongly as I possibly can -- do not try to design this product.
Engineering is not the science behind building. It is the science behind not building.