Three-dimensional effects of symmetrically compressing an O-ring with rigid plates are investigated. The O-ring is assumed to be an incompressible elastic material and the mixed boundary value problem is formulated within the framework of classical linear elasticity theory. Transversely compressing the O-ring between flat rigid plates increases the toroidal radius and induces a reduction in the O-ring cross-sectional radius. This reduction depends strongly on the conditions of contact between plate and O-ring, and the reduced contact pressure may threaten the integrity of the seal. For O-rings compressed radially inward or outward, most of the radial displacement is accommodated by a change in the toroidal radius with very little actual compression of the ring material. If this effect is not accounted for in the design. of the seal, the contact pressure may nor be sufficient to secure the seal.