We propose a semi-quantitative model of the initiation and early evolution of a mud volcano. Basin modeling was calibrated against our previous seismic interpretation of the Absheron mud volcano and surroundings in the South Caspian Basin on the one hand, analysis of geological samples from seabed and two exploration boreholes on the other. Some input parameters of the model were derived from laboratory testing of samples from the mud volcano and we used a constitutive law obtained from a previous laboratory study showing the extent to which gas exsolution may damage host sediments, eventually leading to mud generation from compacted sediments. The study identified key geological and physical conditions that led to mud volcano formation: coupling diffusion processes with hydrofracturing and fluid advection, we were able to simulate conditions required to generate mud 3.5 km below the Absheron mud volcano. We also modeled mud remobilization up to the seabed using Navier-Stokes equations modified to account for the impact of gas expansion on mud density. Considering density inversion only, simulations indicate that mud would be extruded at the seabed 100 years after its generation, an ascent rate similar to extrusion rates measured at some active mud volcanoes in Azerbaijan, e.g. the Kotyrdag mud volcano. These models considering eruption dynamics provide semi-quantitative support to purely conceptual formation models based on seismic interpretation of subvolcanic stratal geometry.