This chapter presents numerical simulations of large-deformation flexible composite structures, using geometrically nonlinear explicit FEM for deployable booms. For lenticular booms, explicit solvers handle contact in tension/compression/coiling, with long-step analyses matching experiments and negligible kinetic energy. Tubular boom models predict folding moment-displacement curves consistent with tests, with failure indices less than 1 confirming elastic folding. Bistable boom models match folded configurations, with max failure index 0.37, errors from material nonlinearity and residual thermal stress. Explicit FEM effectively addresses large-deformation contact problems.