A lock with a support structure includes a tubular element connected to a handle having a positioning hole and a center hole. The center hole contains a lock set having a rotatable lock core connected to a transmission element. The transmission element has separated first and second sides. A transversally slidable element is installed to the tubular element for receiving a bias pressure of an elastic element, and includes a protruding portion and a bearing portion. The protruding portion can be moved between engaged and non-engaged positions of the positioning hole of the handle. The support structure includes a support portion. If the first side of the transmission element approaches the support portion of the support structure, the bearing portion of the transversally slidable element will approach the second side of the transmission element for limiting the displacement of the transversally slidable element when an external force is applied.