A process for manufacturing elastomeric components of a tire for a vehicle wheel includes feeding a continuous elongated element from a delivery member by exerting a feeding pressure inside the delivery member, rotating a building support around a geometrical rotation axis of the support, carrying out controlled relative displacements between the delivery member and the support to form a tire component, stopping the feeding of the elongated element when formation of the tire component is complete, and exerting a counter-pressure inside the delivery member after stopping the feeding. Rotating the support assists circumferential distribution of the elongated element on the support. Carrying out controlled relative displacements assists transverse distribution of the elongated element on the support. The tire component is defined by a plurality of coils laid in a pre-established deposition pattern depending on a predetermined cross-section outline to be given to the tire component.