The pressure coefficients (α) of the excitonic transitions arising from the conduction (CB) to the heavy (HH) and light (LH) hole sub-bands of a GaSb-AlSb multiple quantum well structure (MQW) grown on a GaAs substrate are determined. Photoreflectance (PR) and Photoluminescence (PL) studies are employed at cryogenic temperatures. The α for the ground sub-band transition is ~10% smaller than that for bulk GaSb. This effect is explained by in-plane deformation of the MQW arising from the substrate under external pressure. On the other hand, the α get progressively smaller for the higher sub-band transitions due to quantum confinement The PL intensity drops dramatically as the direct Γ CB crosses the L CB at ~10kBars but the PR intensity persists until the X CB crosses each sub-band energy.