A saddled vehicle comprising an engine support structure, the structure comprising: a pair of mounted portions provided integrally with an engine and disposed at lateral ends in a vehicle width direction of the engine; a pair of engine supporting brackets disposed at lateral ends in the vehicle width direction of a vehicle body frame and extending to the mounted portions, respectively; and engine mounting portions provided at the supporting brackets, respectively; wherein each of the mounted portions is mounted to a corresponding one of the engine mounting portions with at least one damper member provided therebetween to be independently elastically displaceable, wherein a first one of the engine mounting portion and the mounted portion has a proximal portion and a bolt member screwed to the proximal portion in a screwed direction, the damper member is disposed between a head of the bolt member and the proximal portion, and is tapered and fitted to a second one of the engine mounting portion and the mounted portion in a direction perpendicular to the screwed direction, and the second one of the engine mounting portion and the mounted portion fitted to the outer peripheral surface of the damper member has an inner peripheral surface tapered correspondingly to the outer peripheral surface of the damper member, and in a state where the mounted portion is mounted to the engine mounting portion with the damper member disposed therebetween, the damper member is deformed by compression in the screwed direction between the proximal portion and the head of the bolt member, and is kept deformed by expansion in the direction perpendicular to the screwed direction, and the screwed direction agrees with the vehicle width direction, the at least one damper member has a tuboid shape with a minor radial end and a major radial end, and includes a pair of damper members, and the minor radial ends of the damper members fastened by the bolt member face each other with a constant gap therebetween in the vehicle width direction, and the bolt member includes a shaft having an outer peripheral surface fitted to a collar having a flange and a washer in abutment with an end edge opposite to the flange of the collar, and the damper members are fitted to an outer peripheral surface of the collar, and the flange and the washer are in contact with the end edges in the vehicle width direction of the damper members, and the damper members and the collar are provided separately from each other, outer peripheral surfaces of the damper members are tapered to be gradually decreased in diameter from the major radial ends to the minor radial ends, and the major radial ends of the damper members each have a chamfered portion. a pair of mounted portions provided integrally with an engine and disposed at lateral ends in a vehicle width direction of the engine; a pair of engine supporting brackets disposed at lateral ends in the vehicle width direction of a vehicle body frame and extending to the mounted portions, respectively; and engine mounting portions provided at the supporting brackets, respectively; wherein each of the mounted portions is mounted to a corresponding one of the engine mounting portions with at least one damper member provided therebetween to be independently elastically displaceable, wherein a first one of the engine mounting portion and the mounted portion has a proximal portion and a bolt member screwed to the proximal portion in a screwed direction, the damper member is disposed between a head of the bolt member and the proximal portion, and is tapered and fitted to a second one of the engine mounting portion and the mounted portion in a direction perpendicular to the screwed direction, and the second one of the engine mounting portion and the mounted portion fitted to the outer peripheral surface of the damper member has an inner peripheral surface tapered correspondingly to the outer peripheral surface of the damper member, and in a state where the mounted portion is mounted to the engine mounting portion with the damper member disposed therebetween, the damper member is deformed by compression in the screwed direction between the proximal portion and the head of the bolt member, and is kept deformed by expansion in the direction perpendicular to the screwed direction, and the screwed direction agrees with the vehicle width direction, the at least one damper member has a tuboid shape with a minor radial end and a major radial end, and includes a pair of damper members, and the minor radial ends of the damper members fastened by the bolt member face each other with a constant gap therebetween in the vehicle width direction, and the bolt member includes a shaft having an outer peripheral surface fitted to a collar having a flange and a washer in abutment with an end edge opposite to the flange of the collar, and the damper members are fitted to an outer peripheral surface of the collar, and the flange and the washer are in contact with the end edges in the vehicle width direction of the damper members, and the damper members and the collar are provided separately from each other, outer peripheral surfaces of the damper members are tapered to be gradually decreased in diameter from the major radial ends to the minor radial ends, and the major radial ends of the damper members each have a chamfered portion.