The design of plug flow reactors with variable mass density is examined. Equations which include a two-term constitutive equation for the reaction rate are derived for the flow of liquids and for the flow of ideal gases in steady plug flow reactors. It is shown that the addition of the second term in the constitutive equation can have a significant effect on the calculation of the reactor volume needed to carry out a specific conversion of the reactant. Published experimental plug flow reactor data support the observation that a reaction rate constitutive equation with two terms can provide a good representation of the experimental data for variable mass density reactors. (c) 2014 American Institute of Chemical Engineers AIChE J 60: 4185-4189, 2014