Models are described which simulate the filament winding of thermosetting and thermoplastic' matrix composite cylinders. The models relate the processing conditions (applied temperature, pressure and processing speed) to parameters of interest such as composite temperature, viscosity, manufacturing stresses and strains, void sizes, as well as degrees of cure, fiber position and fiber tension for thermosets, and crystallinity, degrees of consolidation and bonding for thermoplastics. The use of models in selecting the appropriate processing conditions is discussed.