A vertical wave powered air compressor where different parts of the structure are at different depths (and hence static pressures). A plurality of compression stages are stacked one below the other. Each level has two or more chambers. The chambers have a series of check valves or water seals between them. Each passing wave raises and lowers the entire stack. As the stack moves downward, increased water pressure causes water to enter the first chambers at each level compressing the air inside. As the stack returns upward, the decreased water pressure causes water to leave the first chambers allowing the air therein to expand. However, the check valves prevent the air in the second chambers from expanding or escaping back into the first chambers. Another set of check valves allow the air in the second chambers, as it expands, to be forced downward into the next lower first chamber. With each upward and downward movement of the stack, as waves pass, a quantity of air moves downward from stage to stage until, at the bottom, the lowest stage discharges compressed air into a return pipe.