Abstract: A method for erecting substantially dome-like building structures, the method including the steps of arranging elastically deformable reinforcing members on a membrane arranged on the flat and secured to a generally annular foundation, laying a first layer of concrete material on the membrane and reinforcing members and inflating the membrane to assume the desired shape. After the concrete has sufficiently hardened further reinforcing members are arranged on the extrados of the obtained structure and a second layer of concrete material having a thickness greater than the thickness of the first layer of concrete material is layed thereon. The reinforcing members and the two layers of concrete material are connected together. There is also disclosed an apparatus for implementing the above method.