A method of making a lid for a casket comprises providing tooling configured to produce a one-piece, unitary casket lid having a crown, a pie, a rim and a header, providing settable material from which to mold the lid, molding the settable material with the tooling, permitting the settable material to set thereby producing a one-piece, unitary casket lid having a crown, a pie, a rim and a header, and adhesively applying a wood veneer sheet to at least a portion of the lid. The veneer sheet can be applied with either a membrane press or a profile wrapping machine.