Apparatus and methods for curing composite compositions that react with CO2. The apparatus in general includes an easily transportable and easily assembled curing structure, such as a plastic sheet housing supported by gas pressure and/or by mechanical supports. Apparatus for providing reagent CO2, for measuring water content and for removing water, and for controlling temperature, flow rates and flow directions through the curing structure. Examples of curing procedures and examples of cured materials in desired shapes are described.