In this paper we theoretically investigate the role of hydrostatic pressure by analyzing its influence on potential barrier's height in GaAs/AlxGa1−xAs core/shell spherical quantum dots. The values of hydrostatic pressure considered here are always below the Γ−X crossover. In addition, we take into account the barrier shell's size effects and the barrier's aluminum concentration, looking for a description of the features of the intraband optical absorption coefficient in the system. The electronic structure is calculated within the effective mass approximation. From the numerical point of view the hybrid matrix method was implemented to avoid numerical instability issues that appears in the conventional transfer matrix method. The main intersubband optical transition is considered to take place between the 1s and 1p computed electronic states. The results show that the absorption coefficient undergoes first a red-shift and later a more pronounced blue-shift, depending on the AlxGa1−xAs barrier width (wb1). The absorption coefficient experiences a blue-shift as the barrier's aluminum concentration increases, and it is non monotonically red-shifted as the hydrostatic pressure augments, due to the barrier's height pressure dependency. For the chosen system parameters, the absorption coefficient resonant peak lies within the range of 20 to 30 meV, that corresponds to the THz frequency region. Accordingly, this system can be proposed as a building block for photodetectors in the THz electromagnetic spectrum region.