The elasticity of alpha-helices is examined using equilibrium molecular-dynamics simulations. From the statistics of curvatures and twists, we compute the elastic moduli of several representative alpha-helices, both in the presence and absence of aqueous solvent. We discover that the bending modulus (persistence length) of the helices is independent of the amino-acid sequence, although helices in water are slightly softer than in vacuum. The response of the helices under the action of an external force is also computed and compared with continuum mechanics predictions. Within the time scale of our simulation, we show that the properties of alpha-helices are well reproduced by an elastic and isotropic rod. The persistence length (bending modulus) of most alpha-helices in water or vacuum is approximately 100 nm, roughly twice that of DNA.