Abstract: A bumper assembly for a vehicle and the associated vehicle comprising this bumper assembly are described. The vehicle comprises a chassis. The bumper assembly comprises: a bumper core. The bumper core, in turn, comprises: a first cross member made of a first thermoplastic material and a first and a second substantially undeformable connection device for rigidly fixing the first cross member to the chassis of the vehicle. The first and the second substantially undeformable connection devices co-operate with the first cross member. The bumper core also comprises a second cross member and at least one shock absorbing element arranged between the first cross member and the second cross member. The second cross member is connected to said first and second substantially undeformable connection devices or it is formed as one piece with said substantially undeformable connection devices.