To attain compatibility between the steadiness under breaking and the gap absorbing performance at cornering (banking) with a simple structure.

A front fork for motorcycle 4 is provided with a pair of inverted type tubes 42 (outer tube 40 and inner tube 41 situated upward and downward, respectively). The outer tube 40 is connected by an upper bracket 50 and a lower bracket 51. Rigidity of a lower part of a vehicle body than a lower bracket of the outer tube 40 is increased in the direction to the fore-and-aft and decreased in the direction to the left and right.