Tolerance analysis is an important step to validate assembly process planning scenario. Simulations are generally performed to evaluate the expected geometrical variations of the assembled product. When the simulation models take into account part compliance, assembly sequence and contact interaction, the resulting behaviour of the assembly are generally non-linear and simulations – mainly performed using finite element analysis – require high computing efforts. This paper investigates the ability to approximate the non-linear propagation of geometrical variations in assembly with artificial neural networks. The aim is to drastically reduce the computing efforts required for the simulation and therefore allow its use for the geometrical tolerances allocation optimisation. The influence of the neural network design parameters on the approximation quality is presented in a case study. The quality of the neural network approximation is also evaluated and discussed.