The strain hardening and the pre-compressive forces exerted on the ceramic filaments in Ag/Bi2Sr2Ca2Cu3O10+x (BSCCO or Bi – 2223 in short) composite wire is analysed and discussed in detail. Tensile stress–strain σ–ε, hardening – relaxation σ(ε(t)) , and the strain – dependent critical current I (ε) analysis and measurements were carried out on specimen wire at 77 K. An analysis based on fractal C hardening model is presented such that the applied strain starts to exponentially decline at time t = d when normalised σ(t) value equals the value used for the calculation of the composite modulus of elasticity. A biexponential model is further employed over the causally convolved experimental data in order to analyse and compare the relaxation process from both the fractal order and the unnormalised stress range, respectively. Eventually, since the weak metallic part of the composite indicates an abrupt transition from elasticity to direct plasticity, σ–ε data were further analysed by a rate – dependent power – law hardening of the Ramberg – Osgood type. The highest attainable residual strain is therefore used to estimate the intrinsic strain in Bi – 2223 filaments when the pre-compressive stress is completely depleted.