An apparatus for preparing a multi-cellular foamed board of thermoplastic resin which comprises an extruder, a die and a moulding passage, the die having at the forward end thereof an orifice having a broad width with respect to a height thereof, the forward end forming a convex surface which protrudes the greatest in the resin advancing direction at a middle portion in the width direction and retreats progressively away from the middle portion, the moulding passage having a resin passageway therein and a concave surface on the inlet side thereof, the resin passageway communicating with the orifice, the concave surface being engageable with the convex surface of the die so that the moulding passage is closely contacted with the convex surface of the die, and the resin pasageway in the passage being enlarged at a portion close to and extending along the concave surface in the thickness direction and in the width direction toward the resin advancing direction.