Method for removing tires (P) of wheels (R) of vehicles comprising at least the following steps: - supplying a machine for the assembly and removal of tires (P) of wheels (R) of vehicles comprising: - at least one bead breaking tool movable for bead breaking a tire (P) from a rim (H) of a wheel (R) of vehicles; and - at least one rotary gripping unit adapted to support said wheel (R) and set it in rotation around a work axis (B); wherein said bead breaking tool and said rotary gripping unit are mutually movable along a sliding direction (C) substantially transverse to said work axis (B); - bead breaking said wheel (R) by inserting said bead breaking tool between a bead (T', T") of said tire (P) and a flange (F', F") of said rim (H) and by setting in rotation said wheel (R) by means of said rotary gripping unit , during the setting in rotation said bead breaking tool remaining in contact with an internal bearing surface (S', S") of said rim (H); - during said bead breaking, detecting the mutual movement of said bead breaking tool and of said rotary gripping unit along said sliding direction (C) 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 (P) of wheels (R) of vehicles comprising: - at least one bead breaking tool movable for bead breaking a tire (P) from a rim (H) of a wheel (R) of vehicles; and - at least one rotary gripping unit adapted to support said wheel (R) and set it in rotation around a work axis (B); wherein said bead breaking tool and said rotary gripping unit are mutually movable along a sliding direction (C) substantially transverse to said work axis (B); - at least one bead breaking tool movable for bead breaking a tire (P) from a rim (H) of a wheel (R) of vehicles; and - at least one rotary gripping unit adapted to support said wheel (R) and set it in rotation around a work axis (B); - bead breaking said wheel (R) by inserting said bead breaking tool between a bead (T', T") of said tire (P) and a flange (F', F") of said rim (H) and by setting in rotation said wheel (R) by means of said rotary gripping unit , during the setting in rotation said bead breaking tool remaining in contact with an internal bearing surface (S', S") of said rim (H); - during said bead breaking, detecting the mutual movement of said bead breaking tool and of said rotary gripping unit along said sliding direction (C) 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 . <EOS>