Dorsal closure, a stage of Drosophila development, is a model system for cell sheet morphogenesis and wound healing. During closure, two flanks of epidermal tissue progressively advance to reduce the area of the eye-shaped opening in the dorsal surface, which contains amnioserosa tissue. To simulate the time evolution of the overall shape of the dorsal opening, we developed a mathematical model, in which contractility and elasticity are manifest in model force-producing elements that satisfy force-velocity relationships similar to muscle. The action of the elements is consistent with the force-producing behavior of actin and myosin in cells. The parameters that characterize the simulated embryos were optimized by reference to experimental observations on wild-type embryos and, to a lesser extent, on embryos whose amnioserosa was removed by laser surgery and on myospheroid mutant embryos. Simulations failed to reproduce the amnioserosa-removal protocol in either the elastic or the contractile limit, indicating that both elastic and contractile dynamics are essential components of the biological force-producing elements. We found it was necessary to actively upregulate forces to recapitulate both the double and single-canthus nick protocols, which did not participate in the optimization of parameters, suggesting the existence of additional key feedback mechanisms.