A small scale sample nuclear waste package, consisting of a 28 mm diameter uranium penny encased in grout, was imaged by absorption contrast radiography using a single pulse exposure from an X-ray source driven by a high-power laser. The Vulcan laser was used to deliver a focused pulse of photons to a tantalum foil, in order to generate a bright burst of highly penetrating X-rays (with energy >500 keV), with a source size of <0.5 mm. BAS-TR and BAS-SR image plates were used for image capture, alongside a newly developed Thalium doped Caesium Iodide scintillator-based detector coupled to CCD chips. The uranium penny was clearly resolved to sub-mm accuracy over a 30 cm2 scan area from a single shot acquisition. In addition, neutron generation was demonstrated in situ with the X-ray beam, with a single shot, thus demonstrating the potential for multi-modal criticality testing of waste materials. This feasibility study successfully demonstrated non-destructive radiography of encapsulated, high density, nuclear material. With recent developments of high-power laser systems, to 10 Hz operation, a laser-driven multi-modal beamline for waste monitoring applications is envisioned.