Knowledge of urinary stone composition and structure provides important insights in guiding treatment and preventing recurrence. No current method can successfully provide information relating structure and composition of intact stones. We are developing a tomographic technique that uses measures of coherently scattered diagnostic x-rays to yield stone composition. Coherent-scatter (CS) properties depend on molecular structure and are, therefore, sensitive to material composition. Powdered, amorphous or polycrystalline materials with no significant orientation produce circularly symmetric CS patterns. However, in materials with preferred crystallite orientation, like urinary stones, bright spots in CS patterns are observed. This compromises a composition analysis based on comparing CS measurements from calculi to a library of CS signatures from powdered chemicals. We show that a computed tomographic reconstruction of CS measurements using filtered backprojection (CSCT) effectively eliminates bright spots and yields CS patterns equivalent to powdered materials. This allows for direct comparison with a powdered chemical reference library to establish composition. Validation is achieved through a tomographic CS analysis of an aluminium (Al) rod phantom. Much like calculi, CS patterns from a solid polycrystalline Al rod exhibit diffraction spots, absent in the ring-like Al powder CS pattern. We show that the reconstructed Al CS cross-section is equivalent to its powdered counterpart and results in clearly defined composition images. The potential of CSCT to identify stone composition is demonstrated through images of intact stones deemed chemically pure by infrared spectroscopy. Computed tomographic reconstruction of CS signals allowed the generation of composition maps, showing the distribution of stone components. These images provide strong evidence that current laboratory techniques risk missing critical stone components due to inadequate sampling. This is of particular importance since follow-up treatments are based on these composition analyses. CS analysis can distinguish common stone components and can provide topographic composition maps of intact stones. Such details offer invaluable clinical information regarding stone formation, treatment and follow-up, and thus support the development of CS analysis as a laboratory stone analysis technique.