Highly ordered, near-single-crystal lamellar films of a triblock copolymer (polystyrene-polybutadiene-polystyrene, PS/PB/PS) were used to study the deformation mechanism of a structure of alternating glassy-rubbery layers, at different orientations of the deformation axis relative to the layer normal. Synchrotron radiation was used for simultaneous in-situ deformation and small-angle X-ray scattering measurements. These were augmented with direct imaging of the structure by transmission electron microscopy. The deformation mechanism depends on the orientation of the force with respect to the structure. Loading parallel to the lamellae results in yielding by propagation of a stable macroscopic neck. The glassy PS layers break up at the neck front, releasing the rubbery layers to achieve high strain. The morphology that develops by deformation of the structure in other directions is an ensemble of new tilt boundaries oriented along the deformation axis. The lamellar normals tilt away from the deformation axis with increasing strain, keeping the lamellar spacing essentially constant. The effect of force applied perpendicular to the lamellae is to fold the layers into a "chevron" morphology, similar to other layered systems such as smectic liquid crystals. At high strain, plastic deformation and fracture of the glassy PS hinges of the "chevron" structure leads to symmetric kink boundaries parallel to the force axis. In addition, nucleation of kink band's around defects and propagation of the kink boundaries into adjacent regions can lead to a similar morphology. The lamellar spacing remains constant during perpendicular stretching, and the tilt angle of the lamellar normal follows the macroscopic deformation in an affine manner. Stretching at 45 degrees forms asymmetric kink boundaries parallel to the force axis. The major limbs of the kink band tilt with increasing strain so that the angle between the lamellar normal and the force axis increases from its initial value of 45 degrees, while the lamellar period remains constant. The minor limbs tilt in the opposite direction and exhibit dilation of the lamellar spacing. Eventually the layers rupture, forming voids at the kink-boundary interfaces. The tilt angle of the major-limb lamellae, as a function of strain, is less than predicted by the affine model. This study suggests a general deformation mechanism for a lamellar structure of alternating glassy and rubbery layers. The layered structure responds to deformation, in any direction other then parallel;to the layers, by creating new internal tilt-grain boundaries parallel to the deformation axis. At higher strain the layers yield and subsequently fracture at the kink-boundary interfaces. With increasing strain the lamellar stacks between the kink boundaries tilt toward the deformation axis until they are nearly parallel to it. Since the main features of this mechanism are independent of the initial orientation angle of the layers relative to the deformation axis, it is relevant also to polygranular, globally unoriented lamellar structures.