Damage in polymer matrix composite materials has been formulated in this thesis. The number of model parameters in this formulation has been reduced to the minimum possible one to decrease the number of expensive experimental tests required for setting parameters. To this aim, tensor formulation has been utilized, because the independence of the tensor formulation from the selection of the coordinate system reduces the number of model parameters. Furthermore, the damage evolution rule has been formulated using thermodynamics of irreversible processes, which reduce the number of model parameters needs for setting the damage evolution rule. Using thermodynamically consistent evolution rule requires that the damage surface has been formulated based on the damage energy release rate (DERR) and stress components. Accordingly a novel damage surface with tensor characteristics has been proposed. This new failure criterion has been compared with both the Tsai-Wu and experimental data for a number of composite materials. After the initial assessment of the criterion, it has been used as the damage surface in a damage mechanics formulation using thermodynamically consistent evolution rule. The model has been developed for the general elastic-plastic-damage state. For the present material however, the plastic deformation in glass/polyester pultruded composite beams has been neglected and the formulation has been reduced to the elastic-damage state. This model has been firstly verified for an individual element under three basic loadings, i.e. tensile, compressive and simple shear loadings. Then the model has been used for predicting the damage caused by low-velocity impact loadings. The simulation results predict the damaged region and force-time curve of the impact event in relatively good agreement with the experimental results. Keywords Continuum damage mechanics (CDM), thermodynamics of irreversible processes, low velocity impact