Abstract Elastic stability of fibers in fiber-reinforced composite materials subject to compressive loading is studied. The transversal buckling mode is considered, and two limiting cases, the dilute and non-dilute composites are analyzed. In the case of a non-dilute composite, the cylindrical model and the lubrication approximation are applied. The original problem is reduced to a problem of stability of a rod on elastic foundation. Through the solution of this problem a simple formula for the buckling load is obtained. In the case of a dilute composite, the solution of a problem of stability of a compressed rod in elastic plane is used. On the basis of the obtained solutions in two limiting cases the interpolation formulae are derived. These formulae describe buckling of fiber in the fiber-reinforced composite for any value of the fiber volume fraction. Comparison with known numerical and experimental results is carried out, and the sufficient accuracy of the derived formulae is demonstrated.