When simulating systems of particles embedded in a Stokes flow, it is necessary to question the treatment of close interacting particles. Indeed, when two solids come close one to another, it becomes difficult to approximate the velocity and pressure fields which become singular. However, taking the corresponding singu-larity is essential, both from a numerical and physical point of view. Moreover, experimentalists now need more and more precise results, taking into account the effect of these interactions on the whole flow. The method we propose is based on a decomposition of the fluid/particle problem into two subproblems: a singular problem (when the distance between the particles goes to zero) and a regular problem. The singular field is supposed to be known and the resolution of the problem comes back to solving the regular problem. A first approach have been proposed in [6], where the singular field is tabulated. Here, we propose a new method, based on an asymptotic expansion of the singular field. This method allows to catch the effect of the lubrication on the whole velocity and pressure flows and can deal with any forms of particles. We focus on a toy problem in two dimensions to present the method. Numerical results are given, using a finite element discretization.