A shock absorbing member for a vehicle is designed to absorb the impact energy in a plastic deformation manner to absorb the axial compressive load. The shock absorbing member includes a hollow member whose cross-section is roughly constant and whose axis is adapted to extend forward and rearward of the vehicle. A flange is formed on the hollow member roughly along the axis of the hollow member and projects by an amount increasing gradually from one side toward the other side of the axis.