Abstract : Singularity is a major problem for parallel robots as in these configurations the robot cannot be controlled, and there may be infinite forces/torques in its joint, possibly leading to a robot breakdown. In the recent years classifcations and detection of singularities have made a large progress. However, the issue of closeness to singularity is still open and we propose in this thesis an approach that is based on a static analysis. Our measure of closeness to singularity is based on the very practical issue of having the joint forces/torques lower than a given threshold. We first consider a planar robot whose end-effector has a constant orientation and is submitted to a know wrench and we show that it is possible to compute the border of the region that describes all possible end-effector location for which the joint forces are lower that the fixed threshold. As computing this region appears difficult for non-planar mechanism with our first algorithm, we propose a second algorithm that allows one to compute it by using interval analysis.