This article proposes a universal procedure for efficiently modelling the flexible behaviour of pre-stressed cables, guided by multiple pulleys. Such cable-pulley systems usually connect various structural components, which often feature additional flexibility. One concern in holistic system analyses is to correctly describe the elasticity of the entire assembly for one particular spatial configuration. This can be achieved in terms of a linear stiffness matrix that accounts for the kinematics of the assembly. In this article, parametric stiffness matrices for arbitrary cable-pulley arrangements are derived. A reduction scheme is used to facilitate the integration of the derived stiffness matrix into superordinate finite element models. The method is validated with a non-linear finite element model and applied to a complex hoisting cable system connecting multiple large steel structures.