Abstract: This talk deals with the numerical solution of Timoshenko beam network models, i.e., Timoshenko beam equations at each edge of the network, coupled at the nodes of the network by rigid joint conditions. A prominent application of such models is the simulation of fiber-based materials such as paper or cardboard. Through hybridization, we can equivalently reformulate the problem as a symmetric positive definite system of linear equations posed at the network nodes. This is possible because the nodes to which the beam equations are coupled are zero-dimensional objects. To discretize the beam network model, we apply a hybridizable discontinuous Galerkin method that can achieve arbitrary orders of convergence under mesh refinement without increasing the size of the global system matrix. As a preconditioner for the typically very poorly conditioned global system matrix, we employ a two-level overlapping additive Schwarz method. We prove uniform convergence of the corresponding preconditioned conjugate gradient method under appropriate connectivity assumptions on the network. Numerical experiments demonstrate the practical performance of the method.