A reduction method for constructing vapor-liquid equilibrium phase envelopes with cubic equations of state is presented. The paper describes the calculation procedures for saturation (dewpoint/bubblepoint) pressures and temperatures, quality lines (for given mole fraction or volume fraction of one of the equilibrium phases), cricondentherm and cricondenbar points, the critical point, and the spinodal. The phase envelope construction is fully automatic. The saturation points are calculated throughout the critical region by stepping around the phase envelope in pressure or temperature increments. An extrapolation procedure taking advantage of the Jacobian matrix available from a previous step is used. Problem formulation in terms of reduced variables leads to simpler partial derivatives with respect to pressure and temperature. The proposed method is successfully tested for several representative hydrocarbon mixtures with various phase envelope shapes.