What arethe types or say other way from which we can test unfired pressure vessels?

Hydro static testing is the most commonly used procedure for checking the performance of pressures vessels. This testing is especially brought into play to verify pressure vessels like cylinders, boilers and tubes either they have leaks or manufacturing flaws that may result in leakage.

like that what are the other types of testing, For example if we want use toxic material what should be the test after its manufacturing.

For pressure testing, pumping it up to the maximum rated PSI with the liquid it is designed for and hold the pressure for an extended period of time.

For toxic materials, you should design a test piping system that contains all of the materials that it might be exposed to including valves, washers and flanges. Then produce a list of acceptable products and materials that the tank can be used with.