A transient analytical, multi-phase, thermodynamic model of foam insulated liquid hydrogen tank is developed to understand the effect of insulation thickness on the evolution of tank pressure and liquid thermal stratification. The model is validated with experimental data reported in literature. Analyses are carried out for pressurization considering two scenarios: first case with tank vent port closed after pressurization to study the pressure evolution and the second case for a constant tank pressure of 3.0 bar to study the growth of liquid thermal stratification. Both cases are investigated for different tank insulation thicknesses of 10 mm, 20 mm, 30 mm and 40 mm and with a pressurization gas temperature of 50 K. Effects of variations in ambient wind velocity and presence of solar flux on self-pressurization profile of the tank are also analysed. The study shows that the reduction in insulation thickness leads to increase in stratified mass. The study also brings out significant increase in pressure rise when tank is insulated with lower insulation thickness.