In statically indeterminate timber structures, the stiffness of the members and the semi-rigid behaviour of joints influence the force distribution in the structure, affecting its performance and reliability. With the ambition to provide a reliable basis for the increasing interest in building more complex and statically indeterminate timber structures, this paper aims at identifying the impact of connections on the reliability of such structures by performing a study of a simple statically indeterminate system, i.e. a simple beam with rotational springs at its supports. Using UQlab, a Matlab-based toolbox, a parametric study varying the stiffness and the level of ductility of connections is performed. Different methods such as Monte Carlo Simulations, Subset, Importance Sampling and Adaptive Kriging with Subset simulation are applied and compared p8in terms of efficiency and computational time. Advanced modelling strategies such as importance sampling are effective means to reduce computational costs especially in complex models. The sensitivity analyses on 9input parameters reveal that the joint stiffness and ductility are amongst the most important input variables. Moreover, the results showed that an increment in reliability is gained increasing the level of ductility of joints of intermediate and high stiffness.