The present invention is an apparatus with flexible membrane for oil storage and transportation, comprising of outer wall, installation opening, blocking cover, oil inlet, oil outlet and breathing orifice. The membrane is arranged in outer wall and fixed in the installation opening or the fixing part of outer wall. The rest of membrane is separated from outer wall. Valve and quick coupling are arranged in both oil inlet and oil outlet. The chamber made of membrane stores the oil in a sealed condition to let the breathing take place outside the membrane so as to prevent direct breathing of oil with air, reduce breathing loss, protect the environment, minimize oxidation of oil, prevent water from entering oil and improve the quality of oil. Also, it prevents oil vapor from mixing with air to improve the safety of storage and transportation as well as reduce the risk of fire and explosion. The flexible structure of the membrane facilitates the resistance to impact and other outer forces. According to the type of materials to be stored, different membranes can be chosen to store and transport liquid chemicals under low and ordinary pressure. This way of storage and transportation not only is environmental-friendly, safe and energy-saving, but also eliminates most of current oil vapor pollution.