An apparatus for depositing a piece of band-like elastomeric element on a forming support in a process for building a tyre for vehicle wheels. The apparatus operates by feeding a piece of band-like elastomeric element having a predetermined nominal length towards the forming support along a predetermined feeding direction and measuring the actual length of the piece along the feeding direction. If the actual length is lower than or equal to a circumferential length of a deposition surface defined on the forming support, the piece is deposited on the deposition surface while the forming support rotates about a rotation axis thereof. During such deposition the piece is pressed on the deposition surface with a pressing force selected as a function of the actual length.