Cylindrical sample of elastic material with twenty fourth cylindrical inclusions, which have the hexagonal structure, is considered. It is assumed that the sample is under piecewise constant normal load, and the fibers are in perfect contact with the matrix. The boundary conditions of the problem are satisfied exactly with help of the generalized Fourier method. The problem is reduced to an infinite system of linear algebraic equations which is solved numerically by the method of reduction. The analysis of stress distribution in the areas of their greatest concentration is given.