Analytical and numerical methods are used to study the process of motion of domain walls in an individual nanowire consisting of ferromagnetic crystallites with a chaotic crystallographic anisotropy. The influence of magnetostatic interaction on the motion is considered. The force profile of the domain wall pinning, caused by stochastic crystallographic anisotropy, is examined. The magnetization curve is analytically constructed and the coercive force is calculated. The Barkhausen jumps of domain walls are investigated. The result is verified by numerically modeling.