A new approach for the evaluation of the compressive strength of fibrous composites due to microbuckling is considered in this paper. Most of the proposed models, thus far, have tried to improve on the classical analysis by Rosen regarding both phases as separate continua with appropriate interface conditions. In this work the fibrous composite is represented by an inhomogeneous two-dimensional continuum with spatial variation in the axial Young’s modulus to account for fibers and matrix. The periodicity of the microstructure is taken into account by expanding the axial Young’s modulus in a Fourier series with wavelength the average spacing between fibers. The compressive strength is determined by examining the stability of small perturbations superimposed on a uniform applied compressive strain. It is found that the compressive strength depends on the wavelength of initial imperfections and bound estimates for minimum and maximum imperfection sizes are derived. The upper bound corresponds to perfectly aligned fibers without any imperfections and coincides with Rosen’s prediction of the compressive strength, while the lower bound corresponds to the more realistic case of imperfect systems and correlates well with experimental data.