A support structure for an exhaust pipe includes left and right side frames disposed on a lower side of a rear floor and a back panel extending downward from the rear floor joined to rear end portions of the side frames. Reinforcing plates join the back panel on a vehicle rear side in positions facing the rear of the side frames. Stays extending in a rearward direction mount to the respective reinforcing plates and support a bumper member. A muffler disposed below the rear floor and on a front side of the back panel or an exhaust pipe connected thereto, is supported on a vehicle body by a hanger rubber. A flange portion that is formed with a reinforcing plate extends rearwardly and perpendicularly therefrom. A hanger rubber mounts to the flange portion to support the muffler or exhaust pipe.