A bumper beam is roll formed so that it gets a closed cross section with, along the length, constant cross section having at least two closed chambers (15, 16) separated by an essentially horizontal partition wall (14). Each chamber has a side (19), which is turned away from the vehicle, with at least one longitudinal concave portion (20, 21; 22, 23) extending along the entire length and one side (24), which is facing the vehicle, with at least one longitudinal convex portion (25, 26; 27, 28) extending along the entire length. After the roll forming, some portions (32) of the cross section are pressed together vertically or horizontally in order to adapt the deformation properties.