The experimentally determined directions of the maximum horizontal compressive stress SH, max in the western European stress province WESP of the West European platform are mostly oriented northwest with an average azimuth of 325o 26o. The traditional approach to the mathematical modeling of the stress field in the Western Europe lithosphere as well as in other stable lithospheric blocks is based on an elastic model of the medium and boundary conditions that specify stresses and/or displacements at the entire perimeter of the region studied. In the particular case of Western Europe, poorly constrained boundary conditions should be set at the southern in the collision zone of the African and Eurasian plates and eastern boundaries of the region. For this purpose, experimental directions of S H, max are used as constraints on the sought-for solution. However, even if the experimental directions of S H, max agree well with their theoretical estimates, model stress magnitudes are still sensitive to the choice of model boundary conditions.A basically different approach proposed and implemented in this work for determining the field of tectonic stresses uses the experimental directions of SH, max as input information rather than constraints on the sought-for solution. The spatially persisting strike of the SH, max axis makes it possible to construct the field of straight trajectories of principal stresses on the WESP territory. The problem of stress determination is then reduced to the hyperbolic-type problem of integrating the equilibrium equations that does not require postulating constitutive relations, and the boundary conditions are only specified on some part of the boundary of the model region. The lithosphere material can be mechanically anisotropic and inhomogeneous. Stresses t R produced by the ridge push were specified in this work on a segment of the Mid-Atlantic Ridge, and stresses t C due to the Africa-Europe collision were specified in the convergence zone. No boundary conditions are required at the eastern boundary of the region studied. Supposedly, straight trajectories of stresses can be extended into oceanic lithosphere areas adjacent to the continent. The formulation of the problem presented in the paper provides substantial constraints on the collision stresses tC. These constraints directly result from the equilibrium conditions of the Western Europe lithosphere rather than from the plate convergence kinematics in the collision zone. A simple analytical expression obtained for the tensor of global tectonic stresses in the study region indicates that the SH, max magnitude decreases in the NW direction. The minimum horizontal stress in the WESP region is shown to be sensitive to the direction of the collision stresses tC. This stress whose modulus increases in the SE direction is compressive, zero or tensile depending on whether the vector of collision stresses tC deviates westward from the SH, max direction, coincide with it or deviates eastward from it. The modification of the inferred solution incorporating stresses applied at the base of the lithospheric plate is discussed.