A micromechanics study is presented of the matrix cracking of fibres-reinforced ceramic composites when subject to tensile stressing normal to fibres. Stability and/or instability of the straight micro-crack paths is investigated for a periodic array of originally collinear, slowly growing microcracks with fibres located in between the neighbouring micro-cracks tips. The relevant application e.g. refers to matrix cracking in 90° plies of cross-ply ceramic composites. The problem is solved using the technique of distributed dislocations and an approximate fundamental solution for a single edge dislocation lying in a general point between inclusion centres. The Muschelishvili complex potentials and the Galerkin method for a numerical evaluation of coefficients of suitable chosen bas functions are employed. Numerical results are presented showing an influence of mutual microcracks-fibres geometry and the mismatch of elastic properties on micro-crack path stability/instability.