The invention relates to a bumper arrangement with a crossmember and two crashboxes which are in each case connectable on one side to the crossmember on an outer region thereof and are arrangeable on the other side on a vehicle-side longitudinal member. It is distinguished in that the crossmember has a hollow chamber profile with a hollow chamber which is round at least in sections in cross section, which hollow chamber profile is arranged in a crossmember longitudinal axis running perpendicularly to the vehicle center longitudinal axis.