We present a fully nonlinear model of the elasticity smectic-A elastomers, and compare our results with a wide range of experimental observations: extreme Poisson ratios, the in-plane modulus, the modulus before and after threshold to layer rotation in response to stretches along the layer normal, the threshold strain, the characteristic, and singular rotation of layers after the threshold. We calculate the x-ray scattering from rotating layers and compare with available data. The model is derived in two ways: from geometrical constraints imposed by layers on a nematic elastomer, and from application of statistical mechanics to a microscopic model of the effect of crosslink points confined in a corrugated potential.