The salinity of an inland coastal brackish karstic spring is modeled on the basis of a simple concept of fluid exchange through head differences between a continuous porous matrix and a karst conduit. The coastal aquifer is reduced to an equivalent porous medium (matrix) naturally invaded by seawater, crossed by a single karst conduit where fresh water and brackish water mix in variable proportions and flow up into the spring. A new numerical model with an upwind explicit finite difference scheme, called salt-water intrusion in karst conduits (SWIKAC), was developed and successfully applied to the Almyros spring of Heraklio (Crete, Greece). The good fit of the model to the observed salinity in the spring validates the proposed conceptual model of salinization. It provides a quantitative description of the seawater intrusion inside the karst conduit. The results open up new perspectives for managing the fragile and precious fresh water resources in karstic coastal zones.