Preliminary results of a new stochastic model for the self-field effect in large Cable In Conduit Conductors (CICC) are presented. We show that the electric properties of CICC can be inferred by using only one (arbitrary and not necessary exact) strand trajectory. By applying a non-conventional integration technique (Lebesgue) of the electric field along a strand and the Central Limit Theorem we show that all the information is contained in a probability distribution function of one strand trajectory. The model is checked with the measurements done on the SS-FSJS conductor sample. We show that in the high field limit, the critical current of a cable with perfect joints is close to that based on the strand critical current at peak field if there is no current transfer between strands. We demonstrate that for long cables the ergodic hypothesis holds and the strand average can be replaced by the statistical average. (C) 2001 Elsevier Science B.V. All rights reserved.