Will epoxy warp my wood table top, and should I seal the underside?

Epoxy is not structural. It is only as strong as the substrate you apply it to, so whether a table stays flat depends on the wood, not the coating.

A 1/8" flood coat of UltraClear Bar & Table Top Epoxy on a solid, level substrate is not normally a cause for concern. Large coated surfaces are regularly transported to their installation site without warping. Epoxy will not hold a bowed slab flat, though. A board clamped flat and coated will return to its original shape once unclamped, so plane the wood flat and level before you apply epoxy.

When a solid wood top cups or bows after coating, the most common cause is moisture imbalance in the wood rather than the epoxy. The coated top is fully sealed while an unsealed underside can still gain or lose moisture, which creates internal stress. Dense hardwoods like hickory are especially reactive.

To reduce the risk, fully acclimate the wood before you start and seal both top and bottom. You do not need epoxy on the underside or a matching thickness. Oil-based polyurethane is commonly used to seal the bottom; some users use epoxy.

A top that has already cupped can sometimes be improved by acclimating it in a controlled environment, clamping it flat with even counter-pressure and sealing the underside, but results vary and straightening solid wood is not guaranteed.

For river tables that cup because Deep Pour was over-poured onto the slabs, see Deep Pour Epoxy Table Cupping.