The process starts with digging a trench (10) of adequate depth in the slope (8) of the embankment (1) of the existing roadway at a distance corresponding to the widening. A wall (12) is then built in the trench by means of prefabricated elements or by on-site casting, and is subsequently anchored to the road embankment (1) by means of tension elements (17). The wall (12) rises substantially to the level of the roadway so as to define a channel (15) which is then filled with stabilized material, on which the road paving is completed up to the wall.