PROBLEM TO BE SOLVED: To provide a valve gear fitting structure capable of avoiding an abnormal wear.SOLUTION: A valve gear fitting structure comprises: a lash adjustor 25 having an installation part 26 formed at a rocker arm 20, and a plunger 27 slidably mounted on the installation part 26 and having a hemispherical bearing salient 28; a push rod 34 having a semispherical bearing recess 35 for supporting the bearing salient 28 oscillatably; and an intermediate cup 50 interposed between the bearing salient 28 and the bearing recess 35. The contact position (or a first contact position L1) between the bearing recess 35 and the intermediate cup 50 and the contact position (or a second contact position L2) between the intermediate cup 50 and the bearing salient 28 are different from each other. Moreover, the intermediate cup 50 includes: a first oil supply hole 52 extending in the thickness direction at the center position; and a second oil supply hole 53 interposed between the first contact position L1 and the
