A fibre mat as intermediate in the production of moulded pieces with preferably the same wall thickness is disclosed, comprising fibres made overwhelmingly of cellulose which are pressed together with a plastic in a homogeneous mixture. The plastic is in the form of fire with a length in the range of 30-100 mm and the cellulose fibres have a length of 10-100 mm. The cellulose fibres preferably comprise natural fibres, formed from, flax, sisal, hemp, kenaf, technical viscose fibres or mixtures thereof, or from regenerated cellulose, particularly synthetic cellulose obtained from wood.