The eruptive behavior of mud volcanoes has been explored in several forward and inversion models. The forward models, based on classical continuum-mechanics, simulate the non-stationary processes of gas seepage and two-phase gas-mud flow through the conduit of a mud volcano, as well as the quasi-stationary gas frontal drive that pushes mud out, and the subsequent gas escape into the air. Forward modeling is performed with reference to the pressure and temperature dependence of the gas viscosity and compressibility. The inversion for the depth to the mud column base has yielded an unambiguous solution. According to the modeling results, the depths to the mud base and to the gas reservoir are controlled mainly by conduit permeability, while the interval between two successive eruption events depends on the gas/mud viscosity ratio. The modeling has allowed estimates for the mud breccia portion remaining in the conduit by the time of eruption, and for the subsurface volcano thickness inferred using a hydraulic-fracture model of the related gryphon field, and for the rate of gas release at the beginning of an eruption.