Micromechanics of composite materials’ failure has been investigated under static loading by means of acoustic emission (AE) method. The results showed that for samples made of fiberglass with transverse fibers with respect to the applied load, the process of destruction both in the deformation parameters and in the parameters of total AE has two stages of damage accumulation. At the same time the parameter of total AE shows that the process of destruction begins 5–6% earlier than it is shown by the deformation parameter. Also the nature of the total AE change was analysed.