The connection between texture and elastic behavior of ultrafine-grain (250 nm) copper produced by severe plastic deformation is investigated. A previous study indicated that as-processed ultrafine-grain copper has a low elastic modulus (E=115 GPa) which recovers the accepted value (128 GPa) after annealing above 150-200°C. It was proposed that the low modulus was the result of non-equilibrium grain boundaries. In the current study we have found that the anomalous elastic behavior is likely to be the result of a deformation texture formed during processing. The texture was characterized by x-ray pole figure analysis, revealing preferred orientations of 10 random. The orientation distribution function was calculated and incorporated into a Hill approximation of the elastic behavior. Experimental ultrasonic velocities were measured revealing anisotropy consistent with the predictions of the Hill approximation. After annealing above the recrystallization temperature (185°C), texture analysis and acoustic velocity measurements showed isotropy was recovered.