The molecular dynamics method was used to study the influence of elastic uniaxial deformation on the migration velocity of tilt boundaries with misorientation axes [100] and [111] in nickel. The dependences of the migration velocity at a temperature of 1600 K on the misorientation angle were obtained. It is shown that the high-angle [100] and [111] tilt boundaries migrate at approximately the same velocity, while the low-angle [111] boundaries migrate approximately twice as fast as the [100] boundaries. The obtained dependences of the migration velocity of the boundaries on the value of uniaxial deformation in almost all cases turned out to be nonmonotonic and had a maximum at a tension value of about 1%. With a further increase in tension, migration slowed down, which is most likely explained by a decrease in the surface tension of the boundaries and, accordingly, in the driving force due to the finite sorption capacity of grain boundaries with respect to the free volume. Under elastic compression, in most cases, a monotonic decrease in the migration velocity was observed, which is due to a decrease in free space during compression and a decrease in the mobility of atoms at the boundary.