Capillarity is often exploited in self-cleaning, drag reducing and fluid absorption/storage (sanitary products) purposes just to name a few. Formulating the underlying physics of capillarity helps future design and development of optimized structures. This work reports on developing computational models to quantify the capillary pressure and capillary forces on the fibrous surfaces. To this end, the current study utilizes a novel mass-spring-damper approach to incorporate the mechanical properties of the fibers in generating virtual fibrous structures that can best represent fibrous membranes. Such virtual fibrous structures are then subjected to a pressure estimation model, developed for the first time in this work, to estimate the liquid entry pressure (LEP) for a hydrophobic fibrous membrane. As for accurate prediction (and not just estimation) of the capillary pressure, this work also presents an energy minimization method, implemented in the Surface Evolver code, for tracking the air–water interface intrusion in a hydrophobic fibrous membrane comprised of orthogonally oriented fibers. This novel interface tracking algorithm is used to investigate the effects of the membrane’s microstructure and wetting properties on its resistance to water intrusion (i.e., LEP). The simulation method developed in this work is computationally affordable and it is accurate in its predictions of the air–water interface shape and position inside the membrane as a function of pressure. Application of the simulation method in studying effects of fiber diameter or contact angle heterogeneity on water intrusion pressure is reported for demonstration purposes. Capillary forces between fibrous surfaces are also studied experimentally and numerically via the liquid bridge between two parallel plates coated with electrospun fibers. In the experiment, a droplet was placed on one of the polystyrene- or polyurethane-coated plates and then compressed, stretched, or sheared using the other plate and the force was measured using a sensitive scale. In the simulation, the liquid bridge was mathematically defined for the Surface Evolver finite element code to predict its 3-D shape and resistance to normal and shearing forces, respectively, in presence of the contact angle hysteresis effect. Despite the inherent non-uniformity of the fibrous surfaces used in the experiments and the simplifying assumptions considered for the simulations, reasonable agreement was observed between the experiments and simulations. Results reveal that both normal and shear force on the plates increase by increasing the liquid volume, or decreasing the spacing between the plates.