Double-porosity materials were introduced as models for oil and gas reservoirs having both storage and transport porosities, and were at first usually treated as static mechanical systems in order to study the flow patterns of fluids during reservoir pump-down. Because fluid withdrawal normally increases the effective stress acting on the reservoir, it also turns out to be important to study the geomechanics of the reservoir and how changing fluid pressure affects the solid compaction and fluid permeability of these systems. At the microscale, the mechanical properties of the solid constituents and their distribution in space determine the overall macromechanics of the reservoir system. For systems containing two porosities and two types of solid constituents, exact results for all but one (which may be taken as the overall drained bulk modulus of the system) of the mechanical constants can be derived when the constituents' properties are known using methods developed in this paper. For multi-porosity systems, closure of the system of equations remains an open question, although it is clear that the system can always be closed by the addition of further macroscale measurements.