A shock absorbing bumper adapted for mounting on the front and rear ends of a vehicle such as an automobile, comprising an elastic external guard member having sheathed therein a shock absorbing flexible core member and a separately molded elastic decorative facing base provided on the front surface of the external guard member. The elastic facing base is integrally secured to a horizontal recession in the surface of the external guard member by inserting claws at both edges of the facing base into the corresponding holes formed along both upper and lower edges of the recession.
