This paper studies the stability loss of the micro-fiber which is near the convex cylindrical surface. It is assumed that the material of the cylinder is viscoelastic and the fiber has the infinitesimal initial imperfection in the form of the periodical curving. Within the scope of the piecewise homogeneous body model with the use of the three-dimensional geometrically non-linear field equations of the theory of viscoelasticity, a method is developed for the investigation of the evaluation of such imperfections. Using the initial imperfection criterion for stability loss, the numerical results on the critical deformation and critical times are presented and discussed. The micro-fibers are classified by the values of the ratio of a modulus of elasticity of the fiber material to that of the matrix material. (C) 2010 Elsevier Masson SAS. All rights reserved.