New algorithms for the computation of the simultaneous chemical and physical equilibrium involved in simulations of reactive flash operations, calculations of phase diagrams, and the determination of reactive azeotropes are presented. These algorithms are based on the use of the elements balance approach where the mass balance equations and the Gibbs energy minimization problem are solved in terms of the elements balance variables and not in terms of component compositions. The total number of elements, which can be atoms, molecules or groups (radicals), is smaller than the number of components in the reactive system. The reduced number of variables allows the visualization of the phase diagrams for many multicomponent reactive systems in two- or three-dimensional figures. Element fractions which are by definition similar to the component mole fractions, are employed to determine the conditions for the existence of element azeotropes. These conditions are identical to those that apply for nonreactive (conventional) determination. Illustrative examples highlighting various features of the proposed algorithms are presented through four reactive systems.