Method for handling a built green tyre for a subsequent process, said subsequent process comprising at least one of the following: moulding and vulcanisation; treatment of the green tyre surface; wherein a loading position of the green tyre is obtained by supporting at least a lateral portion of the green tyre within a selected loading basket between a plurality of loading baskets, each loading basket having frustoconical shape and having a vertical axis of symmetry; said method comprising: - arranging said green tyre in a transfer device comprising a gripping device, for transferring it to said selected loading basket; - handling said gripping device along a predetermined stroke line in which said gripping device carrying said green tyre, with a longitudinal axis thereof arranged vertically, is handled along a first horizontal axis up to a predetermined transfer position overlying the selected loading basket at a predetermined height with respect to it; - handling said gripping device according to a vertical axis by performing a downward stroke towards said selected loading basket from said predetermined transfer position; characterised by - controlling said downward stroke by adjusting a deviation between the longitudinal axis of the green tyre and the vertical axis of symmetry of said selected loading basket to obtain a controlled attitude of said green tyre in said loading position at the end of said controlled downward stroke in which said deviation is lower than a predetermined maximum threshold value; - performing such subsequent process(es) while maintaining said controlled attitude. moulding and vulcanisation; treatment of the green tyre surface; wherein a loading position of the green tyre is obtained by supporting at least a lateral portion of the green tyre within a selected loading basket between a plurality of loading baskets, each loading basket having frustoconical shape and having a vertical axis of symmetry; said method comprising: - arranging said green tyre in a transfer device comprising a gripping device, for transferring it to said selected loading basket; - handling said gripping device along a predetermined stroke line in which said gripping device carrying said green tyre, with a longitudinal axis thereof arranged vertically, is handled along a first horizontal axis up to a predetermined transfer position overlying the selected loading basket at a predetermined height with respect to it; - handling said gripping device according to a vertical axis by performing a downward stroke towards said selected loading basket from said predetermined transfer position; characterised by - controlling said downward stroke by adjusting a deviation between the longitudinal axis of the green tyre and the vertical axis of symmetry of said selected loading basket to obtain a controlled attitude of said green tyre in said loading position at the end of said controlled downward stroke in which said deviation is lower than a predetermined maximum threshold value; - performing such subsequent process(es) while maintaining said controlled attitude. - arranging said green tyre in a transfer device comprising a gripping device, for transferring it to said selected loading basket; - handling said gripping device along a predetermined stroke line in which said gripping device carrying said green tyre, with a longitudinal axis thereof arranged vertically, is handled along a first horizontal axis up to a predetermined transfer position overlying the selected loading basket at a predetermined height with respect to it; - handling said gripping device according to a vertical axis by performing a downward stroke towards said selected loading basket from said predetermined transfer position; characterised by - controlling said downward stroke by adjusting a deviation between the longitudinal axis of the green tyre and the vertical axis of symmetry of said selected loading basket to obtain a controlled attitude of said green tyre in said loading position at the end of said controlled downward stroke in which said deviation is lower than a predetermined maximum threshold value; - performing such subsequent process(es) while maintaining said controlled attitude.