The Theory of Critical Distances (TCD) is a well-established method for predicting the effect of notches and other stress concentration features on the fracture and fatigue strength of materials and structures. It has been applied to fibre composite laminate materials but only in a limited manner: previous work was largely limited to two particular cases: circular holes and sharp cracks, both being loaded in axial tension. Long-fibre composites are increasingly replacing metals in many applications, but they are highly sensitive to stress concentration and damage. The present work aimed to develop a more complete picture of notch effects and to investigate the accuracy of the TCD as a predictive tool for this class of materials. Using a quasi-isotropic carbon-fibre/epoxy laminate, we carried out experiments on samples containing two types of stress concentration (notches and corners), varying notch length from 1 to 10 mm and root radius from 0.5 to 20 mm giving stress concentration (Kt) factors from 1.16 to 3.92. Samples were tested in axial tension, in axial torsion and also in mixed tension/torsion loadings. Finite element analysis (FEA) was used to determine stresses in the vicinity of the notches. Predictions using the TCD with a constant value of the critical distance L, were found to be very accurate for the specimens loaded in tension. Specimens loaded in torsion tended to fail at applied torques which were higher than predicted by the TCD, by factors of the order of two. This difference may be explained by the three-dimensional nature of these stress concentrations. The torsion failures could be predicted accurately by using different constants from those used for tension, but this solution is not satisfactory in the general case and should be investigated further.