I've been designing this vessel which runs in the atmospheric pressure conditions. But I faced some issues after taking atmospheric pressure as the design pressure. I've been getting very low thickness values for the shell. How can I solve this?
I'm not sure what you're trying to solve. If a vessel is designed to hold a gas, but that gas will only be at atmospheric pressure, then the walls can be very thin indeed. No? If the pressure is the same on both sides of the walls of the vessel, the pressure difference, inside and out, is zero. A paper bag can be sealed shut, and it will easily hold air inside, at atmospheric pressure.
Maybe you should follow the design codes for atmospheric tanks. Some examples are API 650, UL-142, EN-14015 or EN 1993-4-2. Read the scopes and decide the one that fits your needs. All these standards have minimum structural thickness. That means that if your calculated thickness is smaller than the minimum structural, you shall adopt the minimum structural thickness in order to be able to construct the equipment.
For full access to API 650 or UL-142 search for "law resource API 650" or "law resource UL-142" at Google. EN-1993-4-2 have also been made available online because of "the right of the citizens to know the laws that govern them".
If your case is really a pressure vessel, you also can find minimum structural thickness in ASME Boiler and Pressure Vessel Code Section VIII Division 1. No free version available online for this one, as far I know.