A new algorithm for pressure sensitivity analysis of azeotropes has been developed. The algorithm applies bifurcation theory together with an are length continuation. This allows not only the compositions of azeotropes to be tracked as they change with pressure, but also all new azeotropes that appear within specified pressure range to be found. The algorithm is very efficient, and the computational time required for the pressure sensitivity analysis is on the order of the time necessary to calculate all azeotropes at constant pressure by using a homotopy method.