Empirical inelastic constitutive material models for composites and testing methodology for parameter determination in these models are analyzed. Short fiber as well as long unidirectional fiber reinforced composites are analyzed in situations when the main sources of inelastic behavior are a combination of (a) nonlinear viscoelasticity; (b) nonlinear viscoplasticity; and (c) microdamage-induced reduction of thermoelastic properties, all three evolving with time and stress. These phenomena are included in a common material model. The necessary tests for model identification are tensile quasistatic loading-unloading tests and creep tests at different stress levels with recorded strain recovery after load removal. The methodology is demonstrated presenting models for (a) shear in layers of [45/-45]s laminates; (b) response of short fiber composites (SMC with glass fiber bundles; composites with natural or man-made cellulosic fibers in bio-based resins).