The effect of annealing on dynamic Young’s modulus, E, of ultrafine-grained (UFG) copper obtained by combined severe plastic deformation (SPD) is investigated. It is established that Young’s modulus in the SPD-prepared samples exceeds that in the coarse-grained fully annealed (CGFA) samples by 10 to 20 %. Isothermal annealing at elevated temperatures between 90 and 630°С leads to a sharp decrease of Young’s modulus for annealing temperatures above 210°С. After annealing at 410°С, the value of E reaches its minimal value that is 35 % lower than E in CGFA samples (total change in E is about 47 % of the initial value). Further annealing at higher temperatures leads to an increase in Young’s modulus. It is shown, that the unusual behavior of Young’s modulus is caused by formation of the <111> axial texture in the SPD-treated samples which then is replaced by the <001> texture during the post-SPD heat treatment.