A railcar flexible gear coupling comprising: two external gears ; and two internal gears meshing with the respective two external gears , wherein: when viewed from a tooth thickness direction, a tooth tip of each of the external gears is formed in such a circular-arc shape having a tooth tip crowning radius (Rb) that a distance from a center axis to the tooth tip is longest at a tooth width direction middle, and the distance from the center axis to the tooth tip is shortest at each of both tooth width direction ends; when viewed from the tooth thickness direction, a tooth root of each of the external gears is formed in such a circular-arc shape having a tooth root crowning radius (Rc) that a distance from the center axis to the tooth root is longest at the tooth width direction middle, and the distance from the center axis to the tooth root is shortest at each of the tooth width direction ends; characterized in that the tooth root crowning radius (Rc) is smaller than the tooth tip crowning radius (Rb); each of the external gears is formed such that a reference tooth height (h0) that is a tooth height at a tooth width direction middle position is smaller than an end tooth height (he) that is a tooth height at a tooth width direction end position; and a ratio of the end tooth height (he) to the reference tooth height (h0) is set to 1.21 or more. two external gears ; and two internal gears meshing with the respective two external gears , wherein: when viewed from a tooth thickness direction, a tooth tip of each of the external gears is formed in such a circular-arc shape having a tooth tip crowning radius (Rb) that a distance from a center axis to the tooth tip is longest at a tooth width direction middle, and the distance from the center axis to the tooth tip is shortest at each of both tooth width direction ends; when viewed from the tooth thickness direction, a tooth root of each of the external gears is formed in such a circular-arc shape having a tooth root crowning radius (Rc) that a distance from the center axis to the tooth root is longest at the tooth width direction middle, and the distance from the center axis to the tooth root is shortest at each of the tooth width direction ends; characterized in that the tooth root crowning radius (Rc) is smaller than the tooth tip crowning radius (Rb); each of the external gears is formed such that a reference tooth height (h0) that is a tooth height at a tooth width direction middle position is smaller than an end tooth height (he) that is a tooth height at a tooth width direction end position; and a ratio of the end tooth height (he) to the reference tooth height (h0) is set to 1.21 or more. when viewed from a tooth thickness direction, a tooth tip of each of the external gears is formed in such a circular-arc shape having a tooth tip crowning radius (Rb) that a distance from a center axis to the tooth tip is longest at a tooth width direction middle, and the distance from the center axis to the tooth tip is shortest at each of both tooth width direction ends; when viewed from the tooth thickness direction, a tooth root of each of the external gears is formed in such a circular-arc shape having a tooth root crowning radius (Rc) that a distance from the center axis to the tooth root is longest at the tooth width direction middle, and the distance from the center axis to the tooth root is shortest at each of the tooth width direction ends; characterized in that the tooth root crowning radius (Rc) is smaller than the tooth tip crowning radius (Rb); each of the external gears is formed such that a reference tooth height (h0) that is a tooth height at a tooth width direction middle position is smaller than an end tooth height (he) that is a tooth height at a tooth width direction end position; and a ratio of the end tooth height (he) to the reference tooth height (h0) is set to 1.21 or more. <EOS>