Problems associated with viscoelastic membrane structures have been do
cumented, e. g., dynamic wrinkling and its effects on fatigue analysis
and on snap loading. In the proposed analysis method, the constitutiv
e equation is approximated by a finite difference equation and embedde
d within a nonlinear finite element spatial discretization. Implicit t
emporal integration and a modified Newton-Raphson method are used with
in a time increment. The stress-strain hereditary relation is formally
derived from thermodynamic considerations. Use of modified strain-ene
rgy and dissipation functions facilitates the description of wrinkling
during the analysis. Applications are demonstrated on an inflated cyl
indrical cantilever and on a submerged cylindrical membrane excited by
waves