The magnetic response of three-dimensional Josephson junction networks to constant or slowly varying external magnetic fields is studied. General equations are written for complex networks made of n elementary cubic cells, each cell containing 12 resistively shunted ideal Josephson junctions. The magnetic-flux distribution in the network is calculated numerically as a function of the external magnetic field for different values of superconducting quantum interference device parameter, network size, and external magnetic-field direction. The magnetic-flux distribution in the network is graphically shown, first for increasing and then for decreasing values of the external magnetic flux.