The present invention is a rod jack apparatus with four vertical legs that form a framework and first and second lower brackets connected to the vertical legs. Two hydraulic cylinders extend upwardly from the lower brackets, pass through a first horizontal plate, and are connected to a second horizontal plate. A primary clamping mechanism is situated on top of each of the two horizontal plates, and a secondary clamping mechanism is attached to the underside of each horizontal plate. The apparatus is configured to receive a polished rod, and the primary and secondary clamping mechanisms are configured to grip the polished rod when activated. The sucker rod assembly is lifted out of the well when the first and second hydraulic cylinders are extended. The invention includes a method of using the apparatus described herein.