We study the elastic properties of rigid fiber‐reinforced composites with perfect bonding between fibers and matrix, and also with sliding boundary conditions. In the dilute region, there exists an exact analytical solution. Around the rigidity threshold we find the elastic moduli and Poisson’s ratio by decomposing the deformation into a compression mode and a rotation mode. For perfect bonding, both modes are important, whereas only the compression mode is operative for sliding boundary conditions. We employ the digital‐image‐based method and a finite element analysis to perform computer simulations which confirm our analytical predictions. ©1995 American Institute of Physics.