Increase in demand of liquefied petroleum gas (LPG) has led to development of LPG facilities throughout the world. The limitation of ASME standard in the design of pressure vessels and reoccurring cases of gas plant, gas cylinder explosions led to this research. In this research, finite element method was used to investigate the displacements, deflections and Von-Mises stresses in a cylindrical liquefied petroleum gas pressure tank with respect to plate thickness at different operating pressures and ambient conditions. A cylindrical pressure tank made of ASTM A516 Grade 70 with thickness; 2mm, 5mm, 10mm, 20mm and 30mm was selected for the analysis with plain strain condition assumptions. ANSYS was used to generate the mesh model of the liquefied petroleum gas pressure tank and conduct the finite element analysis. The displacement, deflection and Von-Mises stress showed an inverse relationship with the tank section shell thickness while varying the LPG pressure; 0.5MPa at 200C, 0.91MPa at 400C and 1.55MPa at 600C respectively. It was also observed that the factor of safety showed a linear relationship with increasing shell thickness. For each operating pressure, a minimum shell thickness was deduced. This minimum thickness was at a Von-Mises stress which falls below the materials yield stress and allowable stress. Therefore, the vessel will not fail once operated at or above the minimum pressure tank shell thickness. The effect of weldment along the seams of vessel was not carried out in this research work. Sharp edges are stress raisers, also there is possibility of stress been developed at the inlet and exhaust valves of the pressure tank. The effect of stress at this points on the vessel were not considered for this research work.