A transient two-phase numerical model is developed to investigate insulation performance of cryogenic propellant tanks using finite difference method. The model includes the mathematical formulations for convective and radiative heat transfer from the ambient, heat and mass transfer across liquid-vapor using twophase formulations. The model is validated with the experimental test data on LH2 tank. Subsequently, analyses are carried out to determine heat in-leak, evaporation rate, evolution of pressure and temperature in ullage of cryogenic tank with different foam insulation thicknesses of 20mm, 25mm, 30mm and 35mm. Analysis shows that tank pressure rise is significantly higher at lower insulation thickness. The present study brings out a correlation between rate of tank pressure rise and foam insulation thickness which shows that LN2 evaporation rate has negligible effect on tank pressure rise for simulated conditions. A minimum foam insulation thickness required for no ice formation over foam outer surface is also suggested in the study.