Press for making large molded pulp objects, which has a raisable and lowerable male mold half, perforated for suction dewatering after dipping into a pulp slurry. The molding surface of said male mold half is coated with an elastomer to preserve even surface contact with the molded pulp object during compression and during thermal expansion or contraction of said mold halves. Advantageous embodiments include vacuum distribution troughs beneath the elastomer layer in the male mold half, multiple wire mesh layers on top of the perforated elastomer layer, and slight lateral adjustability of the otherwise stationary female mold half.