A Monte Carlo approach based on energy potential including interface and volume energies is implemented, for the first time, in the framework of Eulerian interface tracking methods in order to deal with capillary driven two-phase flows. As a first step, the Monte Carlo approach is validated on the 2D Laplace's law showing a first order convergence in space. A better accuracy is obtained compared to the standard Continuum Surface Force and Front Tracking approaches. As a second step, the simulation of the pressure field resulting from the action of the surface tension on complex static interface geometries is considered. These geometries correspond to the early times of the two-particle coalescence process. The two peaks of pressure within the contact zone are shown to be well estimated by the Monte Carlo method even when a very small interface curvature is involved. Indeed, the small scale modeling brought by the Monte Carlo methodology, which accounts for the interface in a Lagrangian manner, provides a description of the surface tension effects at a scale smaller than the Eulerian space scale. This work is a first step in coupling stochastic and deterministic models for the simulation of multiphase flows.Read less <