Electronic devices may be provided with antenna structures such as distributed loop antenna resonating element structures. A distributed loop antenna may be formed on an elongated dielectric carrier and may have a longitudinal axis. The distributed loop antenna may include a loop antenna resonating element formed from a sheet of conductive material that extends around the longitudinal axis. A gap may be formed in the sheet of conductive material. The gap may be located under an opaque masking layer on the underside of a display cover glass associated with a display. The loop antenna resonating element may have a main body portion that includes the gap and may have an extended tail portion that extends between the display and conductive housing structures. The main body portion and extended tail portion may be configured to ensure that undesired waveguide modes are cut off during operation of the loop antenna.