What tissue in animals is responsible for its functions as the mechanical tissue of plants and why?

First, you need to figure out what functions mechanical tissue performs in plants: it gives the body strength, is a support.

Animals have tissue with similar functions. This is bone tissue. Bones are composed of mineral and organic matter, they are strong enough to provide support, and also participate in movement.

Invertebrates lack bone tissue, but they have other devices that perform a supporting function. For example, arthropods have a chitinous cover, while sponges (although they do not have real tissues) have skeletal elements – spicules.