A supporting structure for rocker arms for engine valves includes an engine having a cylinder head, a valve provided on the cylinder head and adapted for either of intake and exhaust purposes, a valve-operating mechanism for operating the valve, the valve-operating mechanism including a rocker arm abutting on the top of the valve, to thereby operate the valve, and a pivotal structure for pivotably supporting one end of the rocker arm. The pivotal structure comprises a ball-like portion, a spherical concave portion shaped in a form substantially correspondent to the ball-like portion and engaged with the ball-like portion, and an elastic member disposed at an aperture end of the spherical concave portion and adapted to hold the ball-like portion in the spherical concave portion.