In a process for producing a moulded part, a plate made of thermoplastic material that contains at least one reinforcement layer made of woven, nonwoven, knitted or braided fabrics, inserts or the like embedded in the plastic matrix is heated up to a temperature in the range of the melting point of the thermoplastic material, then shaped by means of a matrix and a male mould. In order to achieve a high, uniform surface quality that requires no subsequent processing with a rational production process, at least one easily deformable membrane that yields to pressure is arranged on at least one side of the plastic plate at least during the shaping process.