We consider dislocations as vortices in elastic strain field and show that an ordered system of partial dislocations in faulted martensites is analogous to a system of flux lines (supercurrent vortices) in type-II superconductors. The network of interacting partial dislocations can form vortex matter, whose dynamics is controlled by applied stress amplitude and by a degree of quenched and thermal disorder. Experimental results on elasticity and ultrasonic anelasticity of ternary faulted martensites from Cu-Al, Cu-Zn families and from binary Cu-Al system, obtained for temperatures between 6 and 300 K, point to the existence of glassy and liquid states of vortex matter in martensites. We show that the liquid and glassy dynamics of vortex matter and reversible transitions between these states account for a large number of unusual low-temperature anelastic effects in faulted martensites. (C) 2007 Elsevier B.V. All rights reserved.