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"The Uncas was a New Bedford whaleship which was built at Falmouth, Mass. in 1828 and operated out of that port until 1843. New Bedford was her port of registry from 1843 until 1862, when she was sold into the merchant service. "The name derives from that of a sachem of the Mohegan Indians who earned a claim for some reward by siding with the Colonists in their area during the King Philip War. The Le Breton picture of the (Incas depicts her, according to the artist, near the Cape of Good Hope.
Mr. Osgood Williams did some further checking at the Peabody Museum, Salem, Mass. He found the following in "Ship Registers of New Bedford" (Vol. 1, 1796-1850): Uncas: Ship, of New Bedford, registered August 4, 1843. Built at Falmouth in 1828. 412 86/95 tons. Length 112 ft. Bins., breadth 28 ft. 8 ins., depth 14 ft. 4 ins. Two decks, three masts, square stern, no galleries, a male bust head. Previously registered at Falmouth, June 27, 1843. Sold abroad in 1865. In Vol. 2 of the Registers (1850-65) the same details and tonnage are given. The vessel was re-registered on September 21, 1857.
On May 5, 1862 the Uncas was registered as: bark, of Wareham, master, William H. Beese. Owner, William H. Beese, of Wareham, Mass. Sold foreign in 1866. Up to the present time nothing has been found about the original owners at Falmouth during the period 1823-1843.
Sea Breezes 10/68

Update:

The stamp is designed after a lithograph made by Louis Le Breton, and shows the American whaler UNCAS off Cape of Good Hope
She was built at Bar Neck wharf, Woodshole, Falmouth Mass. by the owner/shipbuilder Elijah Swift in 1828 as a whaler under the name UNCAS.
Ship rigged,
Sailed from Falmouth under command of Capt. Henry C. Bunker on 07 November 1828 for the Pacific whaling grounds.
15 July 1831 returned Falmouth with onboard 3,468 barrels of sperm oil.
She made two more whaling voyages for Elijah Swift to the Pacific. On her last voyage to Falmouth, she arrived on 11 May 1843, after discharging she was sold to A.H. Howland, New Bedford.
05 August 1843 she sailed from New Bedford for the Indian Ocean under command of Capt. Gelett, returned 13 April 1846 with onboard 59 barrels of sperm oil, 3,950 barrels of whale oil, and 16,000 lbs bone.
21 September 1857 she made her last voyage for Howland as a whaler (the sixth) from New Bedford to the North Pacific under Capt. William H. Luce, returned 17 June 1861 with onboard 175 barrels of sperm oil, 602 barrels of whale oil, and 4,500 lbs. bone.
1862 She was sold for merchant service. On May 5, 1862, the UNCAS was registered as bark, of Wareham, master, William H. Beese. Owner, William H. Beese, of Wareham, Mass.
Sold foreign in 1866.
(There is a lot of difference between these two years 1862-1866?)
In 1862 the ship was bought by the British Robert Imeray and registered at South Shields. He sold it in 1881 to the Cay brothers, based in the same port. It was probably scrapped around 1885. Data: 406 tons. Dimensions: L 34.46 x W 8.86 x D 5.92 m (according to English register) 413 tons. L 34.36 x W 8.74 x D 4.36 m (according to American register) (A:SoS 8/58)
1880 Was she owned by William Cay & Partners, South Shields, 437 ton, dim. 113.0 x 29.1 x 19.5ft. The only time her place of built is given as Falmouth USA. https://www.crewlist.org.uk/data/viewim ... l&page=555
Till 1885 is she given in Lloyds Register.

Sources: Lloyds Register. History of the American Whale Fishery by Alexander Starbuck Navicula.