A tire dismounting method and machine used in dismounting a tire from a rim. The machine has a frame which diametrically spans one side of the rim flange, and engages diametrically opposite portions of the rim flange to restrain movement of said machine axially of the rim, while the rim and tire assembly are supported freely on a surface. A ram is pivotally supported on the frame adjacent one end thereof for orientation of the ram with its axis generally parallel to the rim axis in operation. The ram has a piston with a presser shoe pivotally carried on its free end for movement in a travel path radially outwardly of and adjacent the rim flanges and generally parallel to the rim axis through a working stroke extending axially beyond the remote rim flange. The ram is supported such that the rim axis can move through a range of about 15.degree. from generally parallel to the rim axis to an acute angle intersecting the rim axis on the machine side thereof. The machine includes springs between the ram and frame for yieldingly biasing the ram toward that end limit of its travel generally parallel to the rim axis. A strap coupled between the springs and ram transmits the spring biasing forces and is removable so that the ram may be pivoted to a storage position against the frame. A pair of outriggers may be mounted to the frame for swinging movement between retracted and extended positions.