A longitudinal inertial force (a) produced by a piston (14) is cancelled by an inertial force (b) produced by a crank shaft (15), and secondarily produced right and left inertial forces (c, d) vibrate the outboard motor main body right and left around an imaginary center of vibration (C). At this time, an elastic body (74) elastically supporting the outboard motor main body on the ship is set in such a manner that tangential (L3-direction) rigidity around the imaginary center of vibration (C) is lower than radial (L2-direction) rigidity around said imaginary center of vibration (C); therefore, said right and left vibration is effectively reduced by the low rigidity of the elastic body (74). Propeller thrusts (e, f) acting in a longitudinal direction (L1-direction) are transmitted to the ship through the elastic body (74). Since the rigidity of the elastic body (74) along this direction is set at a high value, the propeller thrusts (e, f) can be effectively transmitted to the ship.