A multiple use modular apparatus for animals having a tower and a base is disclosed that is light weight, easily assembled and reconfigured, and ballast is added inside the tower and base to stabilize the apparatus. The tower is inserted into the base in a very snug interference fit, and the tower has tiers of rows of recesses around its periphery facing in different directions. Shelf pieces of different sizes and shapes and having protrusions extending from one edge are utilized. The protrusions of the shelf pieces are inserted into the recesses in the side of the tower in a snug interference fit to firmly hold the shelf pieces to the sides of the tower. The shelf pieces may be fastened to the tower in a wide variety of configurations to create steps, walkways and platforms. Pieces of carpet or other material may be fastened to the sides of the tower and to the tops of the shelves, walkways and platforms. The modular apparatus may be used by an animal for exercise, play and resting. The shelves are easily removed and reattached to different positions on the sides of the tower to create the wide variety of configurations of shelves, walkways and platforms that will keep an animal interested in exploring the apparatus. In addition, the pieces may be assembled into complex arrangements having multiple towers, interconnecting walkways and toys mounted on the shelves and platforms.