A method for fitting tires (P) to a driving axle of a vehicle carrying heavy loads, which consists, after having determined the type of journey made by said vehicle, in: when the route is of type A (ascending under load with a driving torque and descending empty with a braking torque), fitting to each driving axle tires such that for each transverse groove (31) in the edge portions (B) of the tread (1), the angle of inclination of the rubber faces (310, 311) delimiting the transverse grooves (31) which first come into ground contact is smaller than the angle of inclination of the rubber face opposite delimiting the same transverse groove, or when the route is of type V (ascending empty and descending under load with a braking torque), fitting to each driving axle tires such that for each transverse groove (31) in the edge portions (B) of the tread, the angle of inclination of the rubber face (310, 311) delimiting said transverse groove which first comes into ground contact is larger than the angle of inclination of the rubber face opposite delimiting the same transverse groove. A tire (P) appropriate for implementing the method described.