The response of a mesoscopic layered structure to deformation normal to the layers is prevalently accepted to occur by an undulation instability, a model which was developed for and tested extensively in liquid-crystalline systems. This model has been applied to a layered block copolymer melt by theoretical considerations [Z.G. Wang, J. Chem. Phys. 100, 2298 (1994)] and extended to alternating glassy/rubbery layers by simulation and theory [D.J. Read , J. Phys. D. 32, 2087 (1999)]. In both cases, an undulation instability at extremely small strain is predicted. In this study we investigate the deformation mechanism of a lamellar block copolymer structure, stretched in the direction perpendicular to the layers, by simultaneous in situ measurements of sample stress and elongation and two dimensional small-angle x-ray scattering, at a strain resolution of 0.5%. Deformed microstructures were also observed ex-situ with scanning probe microscopy. A styrene-butadiene-styrene triblock copolymer of total molecular weight 82 000 g/mol containing 45% styrene, was used. Specimens were deformed at ambient conditions, where the system is characterized as alternating glassy/rubbery layers, at the glass transition temperature (T-g) of polystyrene (PS) where the system is viscoelastic/rubbery and well above the T-g of polystyrene where the system is viscous/rubbery. At ambient temperature, the constraints on the rubbery layers due to covalent bonding to the glassy layers at the interface, do not allow any significant dilation of the layer spacing. The results indicate that the yield point in the mechanical response does not correspond to a critical undulation instability. Rather, the low-strain behavior is dominated by tilting of layers in the vicinity of defects. Deformation of the block copolymer melt, above the T-g of PS, causes the layers to dilate affinely with the macroscopic elongation. The stability of dilated layers with respect to tilting is explained by a model which considers the dominating influence of interfacial tension. The undulation instability is observed only during deformation at about the T-g of PS, in which the system can be described as alternating viscoelastic/rubbery layers.