An elastic cover, adapted to be disposed at a lateral side of an electronic device to cover at least a portion of a transmitting port, includes a body having two shielding sheets. Each shielding sheet includes a first portion close to the other shielding sheet and a second portion away from the other shielding sheet. A turn is formed between the first and the second portions so that a cross-section of the shielding sheet appears as a V shape. An opening of the V shape is adapted to face the lateral side. A slit is formed between the two shielding sheets and adapted to correspond to the transmitting port. A transmitting object is adapted to push the two first portions to enlarge the slit, so as to pass through the body and be plugged into the transmitting port. An electronic apparatus having the elastic cover is further provided.