The invention relates to a building board or a building element having a multilayer structure, preferably wood-based and consisting of at least three bonded to each other layers, wherein a layer (5) is made of a material, preferably wood-based, which consists of vertically oriented (fv) vertical fibres (50) and is formed as a core layer between two covering layers (3, 4) made of a layer, preferably wood-based, material, the vertical fibres (50) are oriented substantially in a vertical direction with respect to the main extension (ed) of the covering layers (3, 4), in the preferred embodiment, the vertical fibre layer (50) comprises a plurality of vertical cavities (6) which completely transverse said layer and are oriented in a direction (hv) in conformity with the vertical orientation (fv) of the vertical fibres (50) of the material, preferably wood, of which said layer (5) is made. A method for producing the inventive building boards and elements is also disclosed.