An original analytical model is presented, which makes it possible to simulate effectively the instant load distribution and stiffness in splines while taking into consideration supporting shafts and bearing arrangements along with positioning errors. Spline geometry is defined based on ANSI B92.1 standard, and includes possible lead crown and tip relief on the teeth, along with position errors. The mesh interface between the splines is simulated by using Winkler foundations distributed on tooth flank surfaces whose stiffness elements are determined from the classic Weber and Banaschek’s formulae for tooth bending, contact and base deflections. Each spline is assimilated to a rigid disc with 6 degrees-of-freedom at their centers. The amplitudes and directions of sliding velocity are derived from rigid-solid kinematics and a Coulomb’s law for friction is used to determine the friction force distribution. The resulting equations of equilibrium are iteratively solved by using a unilateral normal contact algorithm, which verifies that all the contact forces on the teeth are compressive and that no interferences between the mating surfaces occur outside the contact zones. Comparisons with a finite element-based model of splines are shown, which illustrate the potential of the modelling approach and its interest when massive parameter analyses are needed.