In this paper, we attempt to develop a method for the stress analyses in an infinite elastic body containing two neighbouring fibres which are located along two parallel lines, each of them having a periodical curving which is of opposite phase according to the other. The stress distribution is studied when the body is loaded at infinity by uniformly distributed normal forces with intensity p acting in the direction of fibres. The investigation is carried out in the framework of the piecewise homogeneous body model with the use of the three-dimensional geometrically non-linear exact equations of the theory of elasticity. Consequently, in the present investigation the effect of the geometrical non-linearity on the considered stress distribution is also taken into account. The numerous numerical results related to the considered stress distribution and to the influence of the problem parameters on this distribution are given. (C) 2003 Elsevier Science Ltd. All rights reserved.