The formation of sinkholes at the Dead Sea area reflects subsurface cavities formed by salt dissolution. This dissolution is related to the recession of the Dead Sea; the groundwater level and the fresh/saline water interface along the shore decline at a similar rate to the rate of the Dead Sea recession, and brines that used to occupy layers below this interface are flushed out by freshwater. Our finite element modeling shows that dissolution of this salt layer is a plausible mechanism to explain the rapid creation of subsurface holes that collapse and form sinkholes. The positive feedback between the rate of flow, the rate of chemical reaction, and the change in permeability accelerates the dissolution processes and might result in "reactive infiltration instability" which is manifested in "fingers" of cavities, into which fluid is channeled, and salt is dissolved. The spacing between the sinkholes and the rate of their creation is controlled by several factors including properties of lineaments/faults, incoming groundwater flux, the salinity of the incoming groundwater, the rate of dissolution, the effective specific surface area, the permeability of the salt and clay layers, the permeability-porosity relation, the dispersivity, and the thickness of the layers. We show that the creation of sinkholes occurs only under specific conditions. These conditions must cause an unstable dissolution front which then causes formation of cavities and eventually sinkholes. The simulations, which utilized the best estimated parameters of the studied area, yield results that are similar to those exhibited in the field.