To provide an engine unit support structure with excellent vibration damping performance and durability, the engine unit support structure (1) is provided with an engine unit (2) having an engine (22), a mounting base (3) for mounting the engine unit (2) thereon, and a plurality of elastic support bodies coupled to the engine unit (2) and the mounting base (3) to thereby support the engine unit (2), in which the plurality of elastic support bodies include a first elastic support body (4A) disposed under the lower surface (20) of the engine unit (2) in a position closest, than any other of the plurality of the elastic support bodies, to the rotation center of the output shaft of the engine (22) and three or more of second elastic support bodies (4B, 4B, . . . ), and the first elastic support body (4A) is disposed within a closed space X in plan view formed by interconnecting the centers of the neighboring second elastic support bodies (4B, 4B, . . . ).