A process for the continuous preparation of non-expanded honeycomb core from non-precorrugated web involves the progressive corrugation and consolidation of web by a corrugating/consolidating unit containing corrugating and consolidating elongate teeth which traverses a bed unit containing sets of former bars (1 and 4), forming a half cell height of honeycomb on each pass. A plurality of node-antinode demes of the topmost half cell layer being formed are consolidated while new corrugations and associated node-antinode demes are being formed. The process allows for more lengthy consolidation time, a smaller temperature differential between consolidating teeth and the node-antinode demes being consolidated, and further allows the corrugating and consolidation temperatures to be substantially independent of each other. The process may be implemented through use of a corrugating/consolidating unit having a travelling belt containing corrugating and/or consolidating teeth which may be individually and selectively heated. The process and apparatus allow production of honeycomb even from thin thermoplastic web materials at high production rates. In a preferred embodiment, the teeth are radiant energy transmissive teeth associated with a source of radiant energy directed through the teeth toward the bottom, node-antinode contacting face.