A cable pulling machine of the invention includes a frame, a mechanical linkage including first and second links having first and second cable gripping shoes disposed thereon respectively in opposed positions, a latching cylinder actuable to cause the mechanical linkage to pivot on multiple axes to bring the shoes into engagement with a cable disposed therebetween, a main cylinder having one end mounted on the frame and actuable to move the linkage in a manner effective to pull the cable in a pulling stroke once the latching cylinder has brought the shoes into engagement with the cable, and a mechanism for extending and retracting the main and latching cylinders. The machine may also include a mechanism for holding the cable in tension between pulling strokes, such as a pivoting wedge mechanism as described hereafter.