Interfaces in martensites and ferroelastic crystals show internal structures which are not simply the interpolation of the two adjacent domains. These structures can influence solitary front propagation as observed for large depinning forces. They also contribute to local pinning of walls when the applied forces are close to the depinning threshold. Under these conditions, walls propagate in jerks and avalanches. Typical depinning is observed for very small forces in single ferroelastic needle domain. It is shown that jerks occur in elastically driven system both for planar walls (D=2) and for needle tips (which represents a line in the three dimensional crystal, D=1). The experimental power law exponents are ~ -2 for the energy exponent for collective avalanches, -1.3 for the elastic response function and -1.8 for an advancing needle domain in LaAlO3.