Relief valves play an important role in preventing damage to pressurized systems as well as in ensuring safety for those handling such systems. In this paper, we discuss the design of a nonlinear relief valve where an elastomeric dome serves as the pressure-sensing element. Unlike relief valves with a linear pressure versus valve opening response, i.e., which open and close at the same pressure, the nonlinear relief valve opens at a particular pressure say P1 and closes at a lower pressure P2. The nonlinear snap-through behavior of the dome is obtained by architecting a design with a negative stiffness region that is monostable. When fluid is let in through the inlet, pressure variations cause the dome to snap. The snapping of the dome is responsible for the opening and closing of a solenoidal valve for venting out the fluid. The design includes a tuner which can vary the pressure at which the relief valve closes. The choice for selecting the dome design depends on the electro-mechanical coupling methodology as well as fluid-structure interaction. The finite element analysis for the architected dome profile is carried out, and a prototype is constructed to test the functioning of the valve.