A derivation is presented of equations which can be used in the design of high pressure apparatus utilizing multiring support. The use of these equations is illustrated by the design calculation for a multi‐ring apparatus known as the anvil assembly. The particular assembly described uses three rings for external support. This assembly is capable of developing average pressures of 160 000 atm for minimum periods of two weeks. The methods and materials used in the fabrication of the assembly are also presented.