The object is to prevent rotation of the case when a load is applied to the adjusting screw that tends to push in the adjusting screw.The lash adjuster includes a cylindrical case 13 having a bottom 17 and received in a mounting hole 6 formed in a top surface of a cylinder head 2, the case 13 having an internal thread 14 on an inner periphery thereof, an adjusting screw 16 having an external thread 15 on an outer periphery thereof which is in threaded engagement with the internal thread 14 of the case 13, and a return spring 18 disposed between the adjusting screw 16 and the bottom 17 of the case 13 and biasing the adjusting screw 16 in a direction to protrude upwardly from the case 13, the adjusting screw 16 having a protruding end 22 protruding from the case 13 and configured to pivotally support an arm 7 of a valve gear, wherein an anti-rotation protrusion 27 is provided on the bottom 17 of the case 13 which is fitted in a fitting port 26 formed in an inner bottom surface 24 of the mounting hole 6, thereby preventing rotation of the case 13.