Abstract: A peripheral seal for an orifice disc in an orifice fitting. The peripheral seal is made of two seal rings both of hard polymeric material with a high elastic modulus. An outer seal ring has a deep recess to receive both the orifice disc and the inner seal ring. The seal rings form a seal around the orifice disc and an annular carrier containing it, as well as with each other, but they are sufficiently hard material that they will not swell or distort under high pressures and/or high temperatures.