The model of single vortex escape from extended linear defect and subsequent vortex dynamics under the Lorentz force action in a rather thick (d > 2λ) 3D anisotropic superconductor is developed. We consider the case of parallel c-oriented linear defects as well as the case of equidistant linear row of such kind of defects, which represents the dislocation model of low-angle [001] tilt grain boundary in HTS films and bicrystals. The suggested model based on the classical mechanics approach allows to describe behavior of an elastic vortex string in the potential well of linear defect and under the action of Lorentz force on its end within the Meissner current carrying layer and to determine the depinning critical current density at low magnetic fields and temperatures.