In the early nineties, Dvorak (1991), and Dvorak and Procházka (1996), put forward Transformation Field Analysis (TFA), which consists of expressing a linear relationship between either eigenstrains or eigenstresses and on the other hand strains and stresses in a structure. By means of these eigenparameters, mechanical and thermal phenomena in materials can be simulated. In this paper, the TFA is applied to homogenization of nonlinear composites. A very useful numerical tool, the BEM, has been applied to the solution of integral equations. A sample example shows the ability of the procedure proposed. The problem is solved on a unit cell at microscopic level, but more complicated structures of fibers on, say, reference volume elements with stochastically distributed fibers may be studied.