A pressure system specially designed for the study of liquid crystal materials at high pressures up to 4kbar is presented. The pressure system is based on a hydrostatic screw injector and uses either oil or gas as the pressure transmitting medium. The type of measurements which can be performed with the instrument include polarized microscopy, optical spectroscopy, electrooptic and electrical measurements. The different measurements performed place specific constraints on the design of the apparatus and the pressure cells, and details are given. A preliminary study of the smectic A modification of the twist grain boundary phase (TGBA) at high pressures is presented. The pressure versus temperature phase diagram shows (i) a negative gradient of the TGBA/isotropic phase boundary line and (ii) that the TGBAphase does not exist at pressures above about 250 bar. Following Lubensky's analogy between the TGBAphase and type II superconductors, the disappearance of the TGBAphase at high pressure may imply that the Landau-Ginsburg parameterKdecreases with pressure.