The stress versus strain relations and the Poisson's ratios under tension of 4 double-walled carbon nanotubes (DWCNTs) with diameters greater than 1 nm were numerically studied with the molecular dynamics method. The simulation shows that in the elastic range the stress and the strain have nonlinear relation, and the tangent elastic moduli of the DWCNTs decrease from 720 to 570 GPa with increasing strain. As the strain increases, the value of Poisson's ratio changes from 0.3 to 0.17, and the sizes of the DWCNTs have little influences on the Poisson's ratio.