Abstract: A process for building a green tyre for a vehicle wheel includes the steps of: a) building a carcass structure of a green tyre on a forming drum, the carcass structure including at least one carcass ply and a pair of annular anchoring structures, said at least one carcass ply being built by laying circumferentially contiguous strip-like elements; b) toroidally shaping the carcass structure for associating it to a crown structure including at least one belt structure; wherein step a) of building includes at least one step of applying a constraining layer of a green elastomeric material reinforced with fibres oriented substantially perpendicular to the axis of rotation of said forming drum, the green elastomeric material reinforced with oriented fibres exhibiting at 20% of elongation in a direction parallel to the direction of orientation of the above fibres, a strain level higher than or equal to 0.