The invention relates to a method and device for blow moulding containers (2). A preform (1) consisting of a thermoplastic material is first subjected to thermal treatment along a transport path in the vicinity of a heating section (24). The preform (1) is then re-modelled by means of blow pressure inside a blow mould (4) in the container (2). The container (2) is blown with an actual contour under the action of the blow pressure, said contour deviating from a target contour of the container (2) in such a way that after removal from the mould and shrinkage the actual contour of the container (2) substantially adopts the target contour. To achieve this, the blow mould (4) has an inner contour that deviates from the target value course of the outer contour (2) of the container.