An elastic large displacement thick-shell mixed finite element is modified to allow for the calculation of viscoelastic stresses. Internal strain variables are introduced at the element's stress nodes and are employed to construct a viscous material model. First order ordinary differential equations relate the internal strain variables to the corresponding elastic strains at the stress nodes. The viscous stresses are computed from the internal strain variables using viscous moduli which are a fraction of the elastic moduli. The energy dissipated by the action of the viscous stresses is included in the mixed variational functional. The nonlinear quasi-static viscous equilibrium equations are then obtained. Previously developed Taylor expansions of the nonlinear elastic equilibrium equations are modified to include the viscous terms. A predictor-corrector time marching solution algorithm is employed to solve the algebraic-differential equations. The viscous shell element is employed to computationally simulate a stair-step loading and unloading of an aircraft tire in contact with a frictionless surface.Johnson, Arthur R. and Tanner, John A. and Mason, Angela J.Langley Research CenterFINITE ELEMENT METHOD; AIRCRAFT TIRES; VISCOELASTICITY; MATHEMATICAL MODELS; ELASTIC SHELLS; DIFFERENTIAL EQUATIONS; PREDICTOR-CORRECTOR METHODS; STRESS ANALYSIS; MODULUS OF ELASTICITY; EQUILIBRIUM EQUATIONS; ALGORITHMS; NONLINEAR EQUATIONS...