The theoretical strength limit in compression (TSLC) of composite material with two alternating isotropic homogeneous elastic and viscoelastic layers is studied. The investigation is made within the piecewise-homogeneous body model with the use of the Three-Dimensional Linearized Theory of Stability for elastic and viscoelastic materials. It is assumed that there is an initial imperfection in the local curving form of the reinforcing layers along the direction which is inclined to the layers. As the criterion for determination of the TSLC, the case is taken for which the aforementioned imperfections start to increase indefinitely. The numerical results for the TSLC are presented and discussed. According to these numerical results, in particular, the direction (or the surface) along which the fracture in compression takes place, is determined. (C) 2011 Elsevier Inc. All rights reserved.