The paper presents a computational model of the load distribution between elements in a planetary roller screw. The idea of the model is to consider the deformations of rolling elements as deformations of rectangular volumes subjected to shear stresses. The contact deformations of threads and the deformations of screw and nut cores are taken into account by a properly chosen shear modulus. This modulus is computed on the basis of stiffness determined using the finite element method. Based on the relation between displacements and forces differential equations are obtained. The solution to these equations is a hyperbolic function that illustrates the load distribution on the threads between cooperating elements. The following considerations are carried out to assess the suitability of the analytical model for the preliminary design and analysis of this type of transmissions.