Trenching apparatus comprises a cutting device (23), preferably an endless chain cutter, mounted on a prime mover (21) for positioning the cutting device in a trench (18) with the prime mover movable on the ground surface (22) above the level of the trench. Where the cutting device is a chain cutter, the boom projects forwardly and downwardly relative to the direction of cutting the trench, and drive means are arranged to drive the chain in a direction to carry the cutting elements upwardly around the distal end ofthe boom and rearwardly along the upper run (30) of the endless chain cutter (23). In operation the distal end of the chain cutter (23) is positioned against the end face of the trench at the bottom of the trench (18); the prime mover (21) moves the chain cutter forwardly in the trench while operating the chain cutter, so as to produce an undercut (55) in the end face (54) of the trench; and the lifting means (25) lifts the cutting device (23) upwardly from the undercut through the material of the end face so as to cut material from the end face of the trench.