The organic matrix composites (OMC) are widely used in aeronautical industry. The mechanical behaviour of these materials is known to be strain rate and temperature dependent. Therefore it is necessary to take the influence of temperature and strain rate into account in the behaviour models. The mechanical behaviour of OMC can be split into two different parts: a first linear and a second non linear phasis. To predict the evolution of the mechanical behaviour, it is important to evaluate the transition between linear and non linear behaviour with respect to the influence of the strain rate and the temperature. For this purpose, different strain rate and temperature dependent failure criteria and yield stress criteria, available in the literature were considered. These criteria were compared to the experimental results obtained in previous works [1]. Finally a strain rate and temperature dependent criterion was proposed to describe more accurately this transition evolution.