Frozen in a block of ice and awakened 11,000 years later, a woolly mammoth is nursed back to life by a herd of distantly related coos. His existence is discovered by Ian and Ina Stevenson and their friend, Baird, who live a simple life in the hills and dells of the northern Scottish Highlands. When Ina combs the wool from the herd of coos to create exotic yarns, she realizes one animal is much different from the rest. His ragged, fringed coat reminds her of shag carpet, and so the wooly mammoth is named Shag. Shag grows quickly, and he grows so large he fears for the herd's safety and shelters with the Stevensons, who welcome him as a family member into their hearts and home. When megalomaniacal fashion designer Monsieur d'LeFolb and his nine Mo-Dels arrive to stage the ultimate outdoor fashion show in a nearby hamlet, the Stevensons' secret is discovered.
Monsieur d'LeFolb desires Shag for himself, and the planned photo shoots turns into a mammoth hunt. Ina, Ian, and Baird vow to protect Shag from this commercial fascist, who not only desires the exquisite wool but plans to clone the animal for use in age-defying cosmetics.