IN Chicago, Kristyn Caliendo does forward-bends with a Jack Russell terrier draped around her neck. In Manhattan, Grace Yang strikes a warrior pose while balancing a Shih Tzu on her thigh. And in Seattle, Chantale Stiller-Anderson practices an asana that requires side-stretching across a 52-pound vizsla.

Call it a yogic twist: Downward-facing dog is no longer just for humans.

Ludicrous? Possibly. Grist for anyone who thinks that dog-owners have taken yoga too far? Perhaps. But nationwide, classes of doga  yoga with dogs, as it is called  are increasing in number and popularity. Since Ms. Caliendo, a certified yoga instructor in Chicago, began to teach doga less than one year ago, her classes have doubled in size.

Not everyone in the yoga community is comfortable with this.

“Doga runs the risk of trivializing yoga by turning a 2,500-year-old practice into a fad,” said Julie Lawrence, 60, a yoga instructor and studio owner in Portland, Ore. “To live in harmony with all beings, including dogs, is a truly yogic principle. But yoga class may not be the most appropriate way to express this.”

Image Doga at the Seattle Humane Society. Credit... Stuart Isett for The New York Times

Appropriate or not, this is how it works: Doga combines massage and meditation with gentle stretching for dogs and their human partners. In chaturanga, dogs sit with their front paws in the air while their human partners provide support. In an “upward-paw pose,” or sun salutation, owners lift dogs onto their hind legs. In a resting pose, the person reclines, with legs slightly bent over the dog’s torso, bolster-style, to relieve pressure on the spine.