The mechanical lash adjuster is arranged between a cam and one end of the stem of a valve urged by a valve spring. The lash adjuster comprises an unrotatable housing having a thread, a plunger subjected to the force of the cam and formed with a thread in engagement with the thread of the housing, and a plunger spring urging the plunger against the action of the valve spring. The lead and flank angles of the engaging threads are set such that the engagement threads can slidably rotate under a given shaft load applied to the plunger unless the frictional torque TB, generated by the friction between the slidable frictional surface F2 of the plunger and a shaft load transmission member to act on the plunger, exceeds the thrust torque TF imparted by the shaft load to the plunger.