Alpheus Spring Packard was born on February 19, 1839, in Brunswick, Cumberland, Maine.

He was an American entomologist and paleontologist. He graduated from the Maine Medical School at Bowdoin College (M.D., 1864). During the Civil War, he served as assistant surgeon of the 1st Maine Veteran Volunteers and left for the front (1864-1865). After the war, he returned to the study of entomology and was acting librarian and custodian of the Boston Society of Natural History. In 1867, he was appointed one of the curators of the Peabody Academy of Science at Salem. He lectured on entomology and comparative anatomy at the Maine State Agricultural College, the Massachusetts Agricultural College at Amherst, and Bowdoin College. He was the Massachusetts state entomologist (1871-1873) and one of the founders and editor-in-chief of the American Naturalist. In 1878, he was appointed Professor of Zoology and Geology at Brown University in Providence, Rhode Island, a position he kept until his death. He was elected a member of the American Philosophical Society in 1878. In 1898, he was vice-president of the section of zoology of the American Association for the Advancement of Science. He wrote school textbooks, e.g., "Textbook of Entomology" (1898) and "Zoology for High Schools and Colleges" (11th ed., 1904).

In 1867, he married Elizabeth Derby Walcott (1842–1929). He died on February 14, 1905, in Providence, Providence, Rhode Island.