The present invention relates to a rotary elastic coupling fitted with an inner ring and with an outer ring surrounding the inner ring around the periphery by forming an annular slit. An elastomer is provided in the annular slit, which is vulcanised or glued to the inner ring and to the outer ring and fills up the annular slit substantially or completely. The annular slit is meander-shaped around the periphery of the coupling so that radially outward protrusions of the inner ring undercut radially inward protrusions of the outer ring. Around the periphery of the coupling, a relief opening is provided in the elastomer on both sides of the protrusions of the inner ring and on both sides of the protrusions of the outer ring.