We have been interested to measure directly the elastic modulus B associated with isothermal layer compression in a smectic A liquid crystal; we use the experimental set up recently described [1], where we use essentially piezoelectric ceramics transducers to generate the strain and to measure the corresponding stress transmitted through the smectic layers. We have used a sample of octyloxycyano- biphenyl (8-OCB), on typical thickness of 100 μ. The response to a step-like applied strain is also a step-like stress, with a quasi complete exponential relaxation. We first analyse the zero delay amplitude of the stress signal. For dilation smaller than the undulation threshold [2], the stress-strain relationship is linear and gives B = 8.106 cgs at T = 60° C. This value decreases with sample aging, by a factor of 4 after 2 weeks. Above undulation threshold, we do observe a kink in the stress-strain relationship. This kink is associated with the optical appearance of a pattern of parallel or square lines characteristic of the layer undulations. For larger strains, the stresses increase again linearly in strain. We then analyse the time dependence of the observed stress. The relaxation time of stresses is in the range of 20-50 msec. The undulated texture close to threshold relaxes in the same time. We attribute this relaxation to the climb of edge dislocations of small Burgers vector, which have been observed in an other work [3]. The residual stress after complete relaxation corresponds to a residual strain of one half smectic layer, value which cannot be suppressed by the motion of the smallest one layer edge dislocation. For larger strain, quasi permanent texture deformation are produced, always with an almost totally relaxing stress. These plastic deformations may correspond to the trapping of edge dislocations inside the large amplitude layer undulations.