Method for removing tires of wheels of vehicles comprising at least the following steps: - supplying a machine for the assembly and removal of tires of wheels of vehicles comprising: - at least one bead breaking tool (4a, 4b) movable for bead breaking a tire from a rim of a wheel of vehicles; and - at least one rotary gripping unit adapted to support said wheel and set it in rotation around a work axis; wherein said bead breaking tool (4a, 4b) and said rotary gripping unit are mutually movable along a sliding direction substantially transverse to said work axis; - bead breaking said wheel by inserting said bead breaking tool (4a, 4b) between a bead (T', T") of said tire and a flange (F', F") of said rim and by setting in rotation said wheel by means of said rotary gripping unit, during the setting in rotation said bead breaking tool (4a, 4b) remaining in contact with an internal bearing surface (S', S") of said rim; - during said bead breaking, detecting the mutual movement of said bead breaking tool (4a, 4b) and of said rotary gripping unit along said sliding direction to obtain a detected shape of said internal bearing surface (S', S"); - comparing said detected shape with a reference shape of said internal bearing surface (S', S") to identify mismatches between said detected shape and said reference shape; characterized by the fact that: - said method comprises the step of reporting said mismatches; - said comparing comprises a step of assigning at least one angular position to at least one of said mismatches with respect to a reference angular position. - supplying a machine for the assembly and removal of tires of wheels of vehicles comprising: - at least one bead breaking tool (4a, 4b) movable for bead breaking a tire from a rim of a wheel of vehicles; and - at least one rotary gripping unit adapted to support said wheel and set it in rotation around a work axis; wherein said bead breaking tool (4a, 4b) and said rotary gripping unit are mutually movable along a sliding direction substantially transverse to said work axis; - at least one bead breaking tool (4a, 4b) movable for bead breaking a tire from a rim of a wheel of vehicles; and - at least one rotary gripping unit adapted to support said wheel and set it in rotation around a work axis; - bead breaking said wheel by inserting said bead breaking tool (4a, 4b) between a bead (T', T") of said tire and a flange (F', F") of said rim and by setting in rotation said wheel by means of said rotary gripping unit, during the setting in rotation said bead breaking tool (4a, 4b) remaining in contact with an internal bearing surface (S', S") of said rim; - during said bead breaking, detecting the mutual movement of said bead breaking tool (4a, 4b) and of said rotary gripping unit along said sliding direction to obtain a detected shape of said internal bearing surface (S', S"); - comparing said detected shape with a reference shape of said internal bearing surface (S', S") to identify mismatches between said detected shape and said reference shape; - said method comprises the step of reporting said mismatches; - said comparing comprises a step of assigning at least one angular position to at least one of said mismatches with respect to a reference angular position.