The governing equations for static structural membrane force equilibrium, for dynamic structural membrane force equilibrium and for transient strongly coupled fluidstructure interaction force equilibrium between structural membranes and viscous (laminar) fluids are presented. The approach for static and dynamic membrane force equilibrium is applied to a square Hypar membrane of 5 m edge length and ±0.0625 m vertical corner elevation. Furthermore, a steel cable net roof structure that spans over a museum building of 88 m × 52.8 m ground section is computationally represented by a membrane that satisfies stiffness as well as mass conservation in comparison with the steel cable net structure. To obtain sufficient curvature throughout the saddle shaped roof structure two Gaussian bell curves as well as two additional Hyparforms are considered for the overall shape of the cable net, i.e. the computational membrane. The roof structure is exposed to eigenload as well as to external load. Displacement results are shown for the different considered cases. To obtain a more detailed statement on external load due to surrounding flow viscous (laminar) fluid flow around the museum building and across its roof structure is computationally modeled. The procedure to interpolate fluid load onto the structural membrane and vice versa to interpolate structural membrane load onto the adjacent fluid is given.