[en] Full text.Wetting of a solid surface by a liquid is of a vital importance in many industrial process, and more particularly the wettability of fibres presents a major interest in many industrial applications as drying and protection of synthetic fibres, textile industries, cosmetology industry and composite material elaboration. Many mathematical studies on the contact of a liquid on a plane solid surface or container surface. However, we did not find any serious mathematical study with cylindrical surface, like a fibre. We propose in this paper the mathematical modeling of the contact between an axisymmetric drop and cylindrical fibre in vertical geometric position, by using the classical method of the Lagrange multipliers and the variation theory. The case of a horizontal position of the cylindrical fibre was previously studied. A typical case of an axisymmetric solid, very studied and commented in literature, is that of a container bounding a liquid-fluid system. Another case is that of a liquid drop in axisymmetric position in contact with a horizontal rigid cylindrical surface, where the contact line is generally a circle with a specific linear free energy, ω, that is equal to a a constant line tension, σ∞. We previously showed that the total energy is composed by contributions relative to different regions of bulk, and dividing surfaces and lines. The most important energetic contribution for the system is the intrinsic energy of bulk of every phase characterized by ω(v)=-P. Another form of energy present in the system is the gravitation potential energy that is function of the position into the system. The energetic contribution of the exterior field is obtained by integration over the total useful volume of the system including both liquid-fluid boundaries and the three phase contact lines. In absence of gravity, we proved the mean curvature H of a cylindrical surface could be expressed as a divergence: divTu=2H, with Tu=√1+|∇u|2/∇u The capillary problem is then written as: {divTu = λ in Ωa,b; v.Tu = -1 on |x| = b; v.Tu = -cosθ on |x| = a. Where λ, a Lagrange multiplier, is a constant to be determined, v the unit exterior normal to ∂Ω in any oint of the three-phase contact line, τthe unit tangent in the same point of C and θ the contact angle of the liquid drop on teh cylindrical surface S. Let us remember that a is the radius of the cylindrical fibre and 2b the thickness of the liquid drop. The domain Ωa,b is defined by: Ωa,b = {x/a,|x|< b}. In general, we proved the existence and uniqueness of a solution of our problem and in absence of gravity, we numerically resolved the Laplace equation and showed a certain influence of the fibre diameter on teh surface energy of the solid