An element-assembly formulation of multi-zone contaminant dispersal analysis theory is described. In this approach, a flow system is idealized as an assemblage of mass transport elements that model specific instances of contaminant mass transport in the flow system. Equations governing the mass transport phenomena modeled by each element are expressed in terms of contaminant concentration variables that approximate the contaminant concentration at discrete points in the flow system. The imposition of conservation of mass allows these element equations to be assembled to form spatially discrete but temporally continuous equations that govern the system as a whole. Solution options are outlined, examples of application are presented, and a family of computer programs that provide one implementation of the theory is briefly described.