In this technical report, we present a theoretical and numerical model to simulate wave propagation in finite networks of rods with both classical Kirchhoff conditions and Improved Kirchhoff conditions at the nodes of the networks. One starts with the continuous framework, then we discretize the problem using finite elements with the mass lumping technic introduced by G.~Cohen and P.~Joly. Finally, we show an implementation of the obtained numeric scheme in a homemade code written in C++ in collaboration with K.~Boxberger, some results and some error estimates.