The post offices are in or near the path of the full eclipse, which cuts across the United States, from Oregon to South Carolina.
Spokesman Mark Saunders says the postmarks will be unique in some locations, while most will use one designed by the national office. He says some post offices are using the special postmark only on Monday but others are also using it before and after the eclipse.
The post office earlier issued a heat-sensitive eclipse stamp. A touch of the finger transforms the image of a solar eclipse into the moon.