A specially designed falling body viscometer has been used to obtain low shear viscosities of dilute solutions of high molecular weight polyethylene in decalin and for detecting phase transitions at high pressures. The method provides valuable theological data at pressures that correspond to those in lubrication and some extrusion processes. In addition, the method enables detection of phase transitions, such as crystallization, that result in detectable changes in theology. The influence of pressures as high as 0.6 GPa (similar to 80,000 psi) is illustrated here through a study of crystallization, with verification from light scattering and calorimetry.