A tillage machine has an undercarriage that utilizes a triple axle walking beam wheel assembly for each load-supporting wheel assembly of the center section of the machine. Hydraulically powered lift arms are connected with the wheel assemblies to raise and lower the chassis of the machine as the wheel arms are swung downwardly and upwardly relative to the chassis. Each wheel assembly includes a primary walking beam pivoted to the lower end of the wheel arm, and a secondary walking beam pivoted to the rear end of the primary beam. A single front wheel is disposed at the front end of the primary beam, while a pair of wheels are disposed on the secondary beam on opposite fore-and-aft sides of the pivot connection with the primary beam. An abutment on the wheel arm engages a stop on the primary beam upon downward rotation of the wheel arm by a predetermined amount relative to the chassis such that continued downward movement of the wheel arm causes load to shift partially off the front wheel and onto the rear wheels.