Engineered underdominance is one of a number of different gene drive strategies that have been proposed for the genetic control of insect vectors of disease. Here we model a two-locus engineered underdominance based gene drive system that is based on the concept of mutually suppressing lethals. In such a system two genetic constructs are introduced, each possessing a lethal element and a suppressor of the lethal at the other locus. Specifically, we formulate and analyse a population genetics model of this system to assess when different combinations of release strategies (i.e. single or multiple releases of both sexes or males only) and genetic systems (i.e. bisex lethal or female-specific lethal elements and different strengths of suppressors) will give population replacement or fail to do so. We anticipate that results presented here will inform the future design of engineered underdominance gene drive systems as well as providing a point of reference regarding release strategies for those looking to test such a system. Our discussion is framed in the context of genetic control of insect vectors of disease. One of several serious threats in this context are Aedes aegypti mosquitoes as they are the primary vectors of dengue viruses. However, results are also applicable to Ae. aegypti as vectors of Zika, yellow fever and chikungunya viruses and also to the control of a number of other insect species and thereby of insect-vectored pathogens.